tag:blogger.com,1999:blog-1031611926873085402024-03-05T00:45:59.070-08:00Math PrinciplesThis website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life.
This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comBlogger1065125tag:blogger.com,1999:blog-103161192687308540.post-91015731024129108162015-08-28T02:45:00.000-07:002016-01-05T02:57:37.358-08:00Converting from Base 14 to Base 10 Problems, 2<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
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<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA" </span></span></span><br />
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<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 1A0BDC2<sub>14</sub> into Base 10.</span><br /><span style="font-size: small;">
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<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
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<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1A0BDC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 14. Base 14 number is also called tetradecimal system. The
digits of Base 14 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10, 11, 12, and 13 are not accepted as a digit, then we have to substitute a
variable which is A = 10, B = 11, C = 12, and D = 13. Hence, the digits of a Base 14 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and D.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1A0BDC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 14 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 1</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> A </span></span></span>0 B D C 2 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁶ 14⁵</span></span></span></span></span></span></span></span> 14⁴ 14³ 14</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 14¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">4</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁶</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁵</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>(0 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (B x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(D x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (C x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 7529536 + 5378240 + 0 + 30184 + 2548 + 168 + 2 = 12940678</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1A0BDC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>12940678 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-67343715042091487332015-08-27T02:33:00.000-07:002016-01-05T02:43:19.140-08:00Converting from Base 14 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 15DC2<sub>14</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">15DC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 14. Base 14 number is also called tetradecimal system. The
digits of Base 14 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10, 11, 12, and 13 are not accepted as a digit, then we have to substitute a
variable which is A = 10, B = 11, C = 12, and D = 13. Hence, the digits of a Base 14 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and D.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">15DC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 14 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 1 5 D C 2 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁴ 14³ 14</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 14¹ 14</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (5 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(D x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (C x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">14</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 38416 + 13720 + 2548 + 168 + 2 = 54854</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">15DC2<sub>14</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>54854 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-54052745088476888512015-08-26T02:18:00.000-07:002016-01-05T02:32:09.696-08:00Converting from Base 10 to Base 14 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 6995483 into Base 14.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 14 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12, and 13. Since 10, 11, 12, and 13 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10, B = 11, C = 12, and D = 13. Hence, the digits of Base 14 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, and D. If
you see a subscript of 14 at the given number, then that number is
written in Base 14. Base 14 number is also called tetradecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 14. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 14 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 499677</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 499677, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 499677</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 499677 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 35691 + R(3)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 35691 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">6995483</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 499677</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 499677 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 35691 + R(3)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 35691</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 2549</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 2549</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 182 + R(1</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 182</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 13 + R(0)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 13</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 0 + R(13 or D)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 14 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 6995483</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>D01535</b><sub><b>14</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-77702446986281327202015-08-25T02:06:00.000-07:002016-01-05T02:15:28.607-08:00Converting from Base 10 to Base 14 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 74569 into Base 14.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 14 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, 12, and 13. Since 10, 11, 12, and 13 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10, B = 11, C = 12, and D = 13. Hence, the digits of Base 14 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, C, and D. If
you see a subscript of 14 at the given number, then that number is
written in Base 14. Base 14 number is also called tetradecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 14. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 14 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 5326</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 5326, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 5326</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 5326 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 380 + R(6)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 380 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74569</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 5326</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(5)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 5326 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 380 + R(6)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 380</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 27 + R(2)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 27</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 1 + R(13 or D</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 14 = 0 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 14 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 74569</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>1D265</b><sub><b>14</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-53041132391538703352015-08-24T01:48:00.000-07:002016-01-05T02:58:17.977-08:00Converting from Base 13 to Base 10 Problems, 2<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 24AC1B3<sub>13</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">24AC1B3<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 13. Base 13 number is also called tridecimal system. The
digits of Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10, 11, and 12 are not accepted as a digit, then we have to substitute a
variable which is A = 10, B = 11, and C = 12. Hence, the digits of a Base 13 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">24AC1B3<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 13 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 2</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 4 </span></span></span>A C 1 B 3 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁶ 13⁵</span></span></span></span></span></span></span></span> 13⁴ 13³ 13</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 13¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁶</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (4 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁵</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>(A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (C x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (B x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (3 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 9653618 + 1485172 + 285610 + 26364 + 169 + 143 + 3 = 11451079</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">24AC1B3<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>11451079 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-47322149697835654822015-08-23T01:36:00.000-07:002016-01-05T01:45:33.960-08:00Converting from Base 13 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert A12BC<sub>13</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A12BC<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 13. Base 13 number is also called tridecimal system. The
digits of Base 13 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10, 11, and 12 are not accepted as a digit, then we have to substitute a
variable which is A = 10, B = 11, and C = 12. Hence, the digits of a Base 13 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, and C.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A12BC<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 13 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: A 1 2 B C </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁴ 13³ 13</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 13¹ 13</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (B x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (C x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">13</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 285610 + 2197 + 338 + 143 + 12 = 288300</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A12BC<sub>13</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>288300 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-20507675743030421202015-08-22T01:22:00.000-07:002016-01-05T02:16:57.716-08:00Converting from Base 10 to Base 13 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 8745699 into Base 13.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 13 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, and 12. Since 10, 11, and 12 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10, B = 11, and C = 12. Hence, the digits of Base 13 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, and C. If
you see a subscript of 13 at the given number, then that number is
written in Base 13. Base 13 number is also called tridecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 13. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 13 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 672746</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 672746, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 672746</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 672746 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 51749 + R(9)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 51749 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">8745699</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 672746</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 672746 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 51749 + R(9)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 51749</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 3980</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(9)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 3980</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 306 + R(2</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 306</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 23 + R(7)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 23</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 1 + R(10 or A)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 0 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 13 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 8745699</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>1A72991</b><sub><b>13</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-41155495520797955132015-08-21T01:08:00.000-07:002016-01-05T01:17:53.492-08:00Converting from Base 10 to Base 13 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Newark, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 95876 into Base 13.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 13 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, 11, and 12. Since 10, 11, and 12 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10, B = 11, and C = 12. Hence, the digits of Base 13 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, B, and C. If
you see a subscript of 13 at the given number, then that number is
written in Base 13. Base 13 number is also called tridecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 13. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 13 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 7375</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 7375, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 7375</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 7375 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 567 + R(4)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 567 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">95876</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 7375</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(1)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 7375 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 567 + R(4)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 567</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 43 + R(8)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 43</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 3 + R(4</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 13 = 0 + R(3)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 13 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 95876</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>34841</b><sub><b>13</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-4497361376875371602015-08-20T01:58:00.000-07:002016-01-05T02:59:47.481-08:00Converting from Base 12 to Base 10 Problems, 2<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert A245A3B<sub>12</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A245A3B<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 12. Base 12 number is also called duodecimal system. The
digits of Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10 and 11 are not accepted as a digit, then we have to substitute a
variable which is A = 10 and B = 11. Hence, the digits of a Base 12 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A245A3B<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 12 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A 2 </span></span></span>4 5 A 3 B </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁶ 12⁵</span></span></span></span></span></span></span></span> 12⁴ 12³ 12</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 12¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁶</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁵</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>(4 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (5 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (3 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (B x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 29859840 + 497664 + 82944 + 8640 + 1440 + 36 + 11 = 30450575</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">A245A3B<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>30450575 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-920512429804734882015-08-19T01:42:00.000-07:002016-01-05T01:46:17.955-08:00Converting from Base 12 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 2AB45<sub>12</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2AB45<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 12. Base 12 number is also called duodecimal system. The
digits of Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10 and 11 are not accepted as a digit, then we have to substitute a
variable which is A = 10 and B = 11. Hence, the digits of a Base 12 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2AB45<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 12 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 2 A B 4 5 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁴ 12³ 12</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 12¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(B x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (4 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (5 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 41472 + 17280 + 1584 + 48 + 5 = 60389</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2AB45<sub>12</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>60389 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-16793597082864233212015-08-18T01:24:00.000-07:002016-01-03T01:37:48.073-08:00Converting from Base 10 to Base 12 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 9983624 into Base 12.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 12 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, and 11. Since 10 and 11 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10 and B = 11. Hence, the digits of Base 12 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, and B. If
you see a subscript of 12 at the given number, then that number is
written in Base 12. Base 12 number is also called duodecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 12. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 12 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 831968</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 831968, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 831968</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 831968 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 69330 + R(8)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 69330 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">9983624</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 831968</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 831968 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 69330 + R(8)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 69330</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 5777 + R(6)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 5777</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 481 + R(5</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 481</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 40 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 40</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 3 + R(4)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 0 + R(3)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 12 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 9983624</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>3415688</b><sub><b>12</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-63710274720329708602015-08-17T01:04:00.000-07:002016-01-05T01:18:32.454-08:00Converting from Base 10 to Base 12 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 74512 into Base 12.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 12 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, 10, and 11. Since 10 and 11 are not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10 and B = 11. Hence, the digits of Base 12 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, A, and B. If
you see a subscript of 12 at the given number, then that number is
written in Base 12. Base 12 number is also called duodecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 12. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 12 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 6209</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 6209, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 6209</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 6209 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 517 + R(5)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 517 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">74512</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 6209</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 6209 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 517 + R(5)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 517</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 43 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 43</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 3 + R(7</span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 3</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 12 = 0 + R(3)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 12 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 74512</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>37154</b><sub><b>12</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-23087375935508930412015-08-16T00:38:00.000-07:002016-01-03T00:54:53.154-08:00Converting from Base 11 to Base 10 Problems, 2<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 2A193A4<sub>11</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2A193A4<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 11. Base 11 number is also called undecimal system. The
digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10</span><span style="font-family: Arial,Helvetica,sans-serif;">.
Since 10 is not accepted as a digit, then we have to substitute a
variable which is A = 10. Hence, the digits of a Base 11 number are 0,
1, 2, 3, 4, 5, 6, 7, 8, 9, and A.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2A193A4<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 11 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2 A 1</span></span></span> 9 3 A 4 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁶ 11⁵ </span></span></span></span></span></span></span></span>11⁴ 11³ 11</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 11¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁶</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁵</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (9 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(3 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (4 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 3543122 + 1610510 + 14641 + 11979 + 363 + 110 + 4 = 5180729</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">2A193A4<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>5180729 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-29949962874839255532015-08-15T00:18:00.000-07:002016-01-03T00:32:24.809-08:00Converting from Base 11 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 12A3A<sub>11</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12A3A<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 11. Base 11 number is also called undecimal system. The
digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10</span><span style="font-family: Arial,Helvetica,sans-serif;">. Since 10 is not accepted as a digit, then we have to substitute a variable which is A = 10. Hence, the digits of a Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A.</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12A3A<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 11 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 1 2 A 3 A </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁴ 11³ 11</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">² 11¹ 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11⁴</span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11³</span></span></span></span></span></span></span></span>) + </span></span></span></span></span></span></span></span></span></span></span></span></span></span>(A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11</span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">²</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (3 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">11¹</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span>) + (A x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> = 14641 + 2662 + 1210 + 33 + 10 = 18556</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">12A3A<sub>11</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>18556 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-54278705125388670992015-08-14T23:52:00.000-07:002016-01-03T00:11:25.064-08:00Converting from Base 10 to Base 11 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 1983425 into Base 11.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 11 number is a number whose digits are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a single digit,
then we have to use a variable to substitute a two digit number. In this
case, let A = 10. Hence, the digits of Base 11 number are 0, 1, 2, 3,
4, 5, 6, 7, 8, 9, and A. If
you see a subscript of 11 at the given number, then that number is
written in Base 11. Base 11 number is also called undecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 11. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 11 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 180311</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 180311, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 180311</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 180311 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 16391 + R(10 or A)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 16391 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">1983425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 180311</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(4)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 180311 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 16391 + R(10 or A)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 16391</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 1490 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1490</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 135 + R(5)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 135</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 12 + R(3)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 12</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 1 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 0 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 11 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1983425</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>11351A4</b><sub><b>11</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-67007097396408137712015-08-13T23:28:00.000-07:002016-01-02T23:47:56.051-08:00Converting from Base 10 to Base 11 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 87425 into Base 11.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is 87425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. 87425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> can also be written as 87425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 11 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Since 10 is not accepted as a single digit, then we have to use a variable to substitute a two digit number. In this case, let A = 10. Hence, the digits of Base 11 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and A. If
you see a subscript of 11 at the given number, then that number is
written in Base 11. Base 11 number is also called undecimal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">87425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 11. How? Let's divide 87425</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 11 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">87425</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 7947</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 7947, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">87425</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 7947</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 7947 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 722 + R(5)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 722 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">87425</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 7947</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(8)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 7947 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 722 + R(5)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 722</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 65 + R(7)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 65</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 5 + R(10 or A)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 5</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 11 = 0 + R(5)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 11 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 87425</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>5A758</b><sub><b>11</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-49849311393521671942015-08-12T02:19:00.000-07:002016-01-02T02:27:57.810-08:00Converting from Base 9 to Base 10 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 187452<sub>9</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">187452<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 9. Base 9 number is also called nonary system. The
digits of Base 9 number are 0, 1, 2, 3, 4, 5, 6, 7, and 8</span><span style="font-family: Arial,Helvetica,sans-serif;">. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">187452<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 9 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 1 8 7 4</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 5 2</span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: 9</span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁵ 9⁴ 9³ </span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9² 9¹ 9⁰</span></span></span></span></span></span></span></span></span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(1 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9⁵</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (8 x 9</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁴</span></span></span></span></span></span></span>) + (7 x 9</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">³</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> + </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(4 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9²</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (5 x </span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9¹</span></span>) + (2 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9⁰</span></span>)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> = 59049 + 52488 + 5103 + 324 + 45 + 2 = 117011</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">187452<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>117011 </b></span></span></span></span><br />
</span><br />
<span style="font-size: large;">
</span><br />
<span style="font-size: large;">
<span class="ob_empty"><wbr></wbr></span></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-87668732978568065162015-08-11T02:06:00.000-07:002016-01-02T02:13:44.135-08:00Converting from Base 9 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 285<sub>9</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">285<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 9. Base 9 number is also called nonary system. The
digits of Base 9 number are 0, 1, 2, 3, 4, 5, 6, 7, and 8</span><span style="font-family: Arial,Helvetica,sans-serif;">. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">285<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 9 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 2 8 5 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9² 9¹ 9⁰</span></span></span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(2 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9²</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (8 x </span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">9¹</span></span>) + (5 x 9</span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span>)</span></span></span></span></span></span></span></span></span></span></span> = 162 + 72 + 5 = 239</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">285<sub>9</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>239 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-2147872095164730142015-08-10T01:49:00.000-07:002016-01-02T02:01:54.553-08:00Converting from Base 10 to Base 9 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 385467 into Base 9.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;"> </span>
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span></span></span></span> can also be written as </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 9 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, and 8. If
you see a subscript of 9 at the given number, then that number is
written in Base 9. Base 9 number is also called nonary system. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 9. How? Let's divide </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 9 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 42829 + R(6)</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 42829, as follows: </span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 42829 + R(6)</span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 42829 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 4758 + R(7)</span></span><br /><span style="font-size: small;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 4758 until the quotient is 0 as follows:</span></span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 42829 + R(6)</span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 42829 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 4758 + R(7)</span></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 4758 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 528 + R(6)</span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 528 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 58 + R(6)</span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">58 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 6 + R(4)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 6 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 0 + R(6)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 9 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">385467</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>646676</b><sub><b>9</b></sub></span></span></span></span></span></span></span></div>
<span style="font-size: large;">
<span class="ob_empty"><wbr></wbr></span></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-28685023383673723492015-08-09T01:35:00.000-07:002016-01-02T01:44:44.780-08:00Converting from Base 10 to Base 9 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 891 into Base 9.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is 891</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. 891</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">891</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 9 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, and 8. If
you see a subscript of 9 at the given number, then that number is
written in Base 9. Base 9 number is also called nonary system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">891</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 9. How? Let's divide 891</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 9 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">891</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 99</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(0)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 99, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">891</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 99</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(0)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 99 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 11 + R(0)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 11 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">891</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 99</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(0)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 99 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 11 + R(0)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 11</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 1 + R(2)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 9 = 0 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 9 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 891</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>1200</b><sub><b>9</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-13393268678712233252015-08-08T01:14:00.000-07:002016-01-02T01:25:12.666-08:00Converting from Base 8 to Base 10 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 257413<sub>8</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">257413<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 8. Base 8 number is also called octal system. The
digits of Base 8 number are 0, 1, 2, 3, 4, 5, 6, and 7</span><span style="font-family: Arial,Helvetica,sans-serif;">. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">257413<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 8 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 2 5 7 4</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1 3</span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: 8</span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁵ 8⁴ 8³ </span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8² 8¹ 8⁰</span></span></span></span></span></span></span></span></span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(2 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8⁵</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (5 x 8</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁴</span></span></span></span></span></span></span>) + (7 x 8</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">³</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> + </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(4 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8²</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (1 x </span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8¹</span></span>) + (3 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8⁰</span></span>)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> = 65536 + 20480 + 3584 + 25 + 8 + 3 = 89636</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">257413<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>89636 </b></span></span></span></span><br />
</span><br />
<span style="font-size: large;">
</span><br />
<span style="font-size: large;">
<span class="ob_empty"><wbr></wbr></span></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-11244325486063747792015-08-07T00:56:00.000-07:002016-01-02T01:09:00.248-08:00Converting from Base 8 to Base 10 Problems<div class="post-body entry-content" id="post-body-4085417946385565184" itemprop="articleBody">
<span style="font-size: small;"><b><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></span></b><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA" </span></span></span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 472<sub>8</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">472<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 8. Base 8 number is also called octal system. The
digits of Base 8 number are 0, 1, 2, 3, 4, 5, 6, and 7</span><span style="font-family: Arial,Helvetica,sans-serif;">. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">472<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 8 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 4 7 2 </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8² 8¹ 8⁰</span></span></span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(4 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8²</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (7 x </span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">8¹</span></span>) + (2 x 8</span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁰</span></span>)</span></span></span></span></span></span></span></span></span></span></span> = 256 + 56 + 2 = 314</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">472<sub>8</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>314 </b></span></span></span></span></span><br />
<br /></div>
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-11620781177955606342015-08-06T00:34:00.000-07:002016-01-02T00:48:06.341-08:00Converting from Base 10 to Base 8 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 299012 into Base 8.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;"> </span>
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span> can also be written as </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 8 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, and 7. If
you see a subscript of 8 at the given number, then that number is
written in Base 8. Base 8 number is also called octal system. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 8. How? Let's divide </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 8 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 37376 + R(4)</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 37376, as follows: </span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 37376 + R(4)</span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 37376 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 4672 + R(0)</span></span><br /><span style="font-size: small;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 4672 until the quotient is 0 as follows:</span></span><br /><span style="font-size: small;">
</span><br />
</span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 37376 + R(4)</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 37376 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 4672 + R(0)</span></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 4672 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 584 + R(0)</span></span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 584 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 73 + R(0)</span></span></span></span></span></span></span></span> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">73 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 9 + R(1)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 9 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 1 + R(1)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 0 + R(1)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></div>
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 8 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">299012</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>1110004</b><sub><b>8</b></sub></span></span></span></span></span></span></span><br />
<span style="font-size: large;">
<span class="ob_empty"><wbr></wbr></span></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-18790116800898067662015-08-05T00:19:00.000-07:002016-01-02T00:28:01.092-08:00Converting from Base 10 to Base 8 Problems<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 987 into Base 8.</span><br />
<br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is 987</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 10. </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span> can also be written as </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub>10</sub>.
If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. The
digits of Base 10 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Base 10
number is a common number that we are using right now in everyday life. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 8 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, and 7. If
you see a subscript of 8 at the given number, then that number is
written in Base 8. Base 8 number is also called octal system. </span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 8. How? Let's divide </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> by 8 as follows:</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 123</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(3)</span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;">Next, let's divide the quotient, which is 123, as follows: </span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 123</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(3)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 123 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 15 + R(3)</span></span><br /><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Do the same thing with 15 until the quotient is 0 as follows:</span></span><br />
<br />
</span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">987</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 123</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"> + R(3)</span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><br />
<span style="font-family: Arial,Helvetica,sans-serif;"> 123 </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 15 + R(3)</span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><br />
<div class="post-body entry-content" id="post-body-993474011296406695" itemprop="articleBody">
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 15</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 1 + R(7)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 1</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span class="_Tgc"><b>÷</b></span> 8 = 0 + R(1)</span></span></span></span></span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> <span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span></span></span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">The remainders will be the digits of Base 8 number. Use the digits of the remainders from bottom to top. Therefore,</span></span></span></span><br />
<br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> 987</span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif; font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>1733</b><sub><b>8</b></sub></span></span></span></span></span></span></div>
<span class="ob_empty" style="font-size: large;"><wbr></wbr></span>Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.comtag:blogger.com,1999:blog-103161192687308540.post-16086676042260365022015-08-04T00:01:00.000-07:002016-01-02T00:13:34.980-08:00Converting from Base 7 to Base 10 Problems, 2<b><span style="font-family: Arial,Helvetica,sans-serif;"><u>Category</u>: Arithmetic</span></b><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><br /></span>
<span style="font-family: Arial,Helvetica,sans-serif;">"Published in Vacaville, California, USA"</span><br />
<br />
<span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Convert 512035<sub>7</sub> into Base 10.</span><br /><span style="font-size: small;">
</span><br />
<span style="color: red;"><span style="font-family: Arial,Helvetica,sans-serif;"><u>Solution</u>:</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">The given number which is </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">512035<sub>7</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> is written in Base 7. Base 7 number is also called heptimal system. The
digits of Base 7 number are 0, 1, 2, 3, 4, 5, and 6</span><span style="font-family: Arial,Helvetica,sans-serif;">. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">On
the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. </span><span style="font-family: Arial,Helvetica,sans-serif;"> If you don't see any subscript at the given number, then that number is
written in Base 10. Base 10 number is also called decimal system. </span><span style="font-family: Arial,Helvetica,sans-serif;">Base 10
number is a common number that we are using right now in everyday life. </span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Now, let's convert </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">512035<sub>7</sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><sub></sub></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> into Base 10. How? Let's multiply each digits by the powers of 7 as follows:</span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Base 6 Digits: 5 1 2 </span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">0 3 5</span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Multiply by: 7</span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁵ 7⁴ 7³ </span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">7² 7¹ 7⁰</span></span></span></span></span></span></span></span></span></span></span> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;">Add all the digits, we have</span><br /><span style="font-size: small;">
</span><br />
</span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(5 x </span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">7⁵</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (1 x 7</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">⁴</span></span></span></span></span></span></span>) + (2 x 7</span></span></span></span></span></span></span></span></span></span></span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">³</span></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">)</span></span></span></span></span></span></span></span></span></span></span> + </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">(0 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">7²</span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">) + (3 x </span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">7¹</span></span>) + (5 x </span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">7⁰</span></span>)</span></span></span></span></span></span></span></span></span></span></span></span></span></span></span> = 84035 + 2401 + 686 + 0 + 21 + 5 = 87148</span></span><br /><span style="font-size: small;">
</span><br />
<span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">Therefore, </span></span></span></span><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-size: large;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;">512035<sub>7</sub></span></span></span></span></span></span></span></span><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"><span style="font-family: Arial,Helvetica,sans-serif;"> = <span style="color: blue;"><b>87148 </b></span></span></span></span><br />
</span><br />
<span style="font-size: large;">
</span><br />
<span style="font-size: large;">
<span class="ob_empty"><wbr></wbr></span></span><br />
Math Principleshttp://www.blogger.com/profile/02762559518712688459noreply@blogger.com