## Monday, August 17, 2015

### Converting from Base 10 to Base 12 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 74512 into Base 12.

Solution:

The given number which is
74512 is written in Base 10. 74512 can also be written as 7451210. 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 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.

Now, let's convert
74512 into Base 12. How? Let's divide 74512 by 12 as follows:

74512 ÷ 12 = 6209 + R(4)

Next, let's divide the quotient, which is 6209, as follows:

74512 ÷ 12 = 6209 + R(4)
6209 ÷ 12 =   517 + R(5)

Do the same thing with 517 until the quotient is 0 as follows:

74512 ÷ 12 = 6209 + R(4)
6209 ÷ 12 =   517 + R(5)

517 ÷ 12 =     43 + R(1)
43 ÷ 12 =       3 + R(7)
3 ÷ 12 =       0 + R(3)

The remainders will be the digits of Base 12 number. Use the digits of the remainders from bottom to top. Therefore,

74512
= 3715412