## Sunday, August 2, 2015

### Converting from Base 10 to Base 7 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 384605 into Base 7.

Solution:

The given number which is
384605 is written in Base 10. 384605 can also be written as 38460510. 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.

On the other hand, Base 7 number is a number whose digits are 0, 1, 2, 3, 4, 5, and 6. If you see a subscript of 7 at the given number, then that number is written in Base 7. Base 7 number is also called heptimal system.

Now, let's convert
384605 into Base 7. How? Let's divide 384605 by 7 as follows:

384605 ÷ 7 = 54943 + R(4)

Next, let's divide the quotient, which is 54943, as follows:

384605 ÷ 7 = 54943 + R(4)
54943 ÷ 7 =   7849 + R(0)

Do the same thing with 7849 until the quotient is 0 as follows:

384605 ÷ 7 = 54943 + R(4)
54943 ÷ 7 =   7849 + R(0)

7849 ÷ 7 =   1121 + R(2)
1121 ÷ 7 =     160 + R(1)
160 ÷ 7 =       22 + R(6)
22 ÷ 7 =         3 + R(1)
3 ÷ 7 =         0 + R(3)

The remainders will be the digits of Base 7 number. Use the digits of the remainders from bottom to top. Therefore,

384605 = 31612047