## Sunday, August 9, 2015

### Converting from Base 10 to Base 9 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 891 into Base 9.

Solution:

The given number which is 891
is written in Base 10. 891 can also be written as 89110. 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 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.

Now, let's convert
891 into Base 9. How? Let's divide 891 by 9 as follows:

891 ÷ 9 = 99 + R(0)

Next, let's divide the quotient, which is 99, as follows:

891 ÷ 9 = 99 + R(0)
99 ÷ 9 = 11 + R(0)

Do the same thing with 11 until the quotient is 0 as follows:

891 ÷ 9 = 99 + R(0)
99 ÷ 9 = 11 + R(0)

11 ÷ 9 =   1 + R(2)
1 ÷ 9 =   0 + R(1)

The remainders will be the digits of Base 9 number. Use the digits of the remainders from bottom to top. Therefore,

891
= 12009