## Monday, August 10, 2015

### Converting from Base 10 to Base 9 Problems, 2

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 385467 into Base 9.

Solution:

The given number which is
385467 is written in Base 10. 385467 can also be written as 38546710. 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
385467 into Base 9. How? Let's divide 385467 by 9 as follows:

385467 ÷ 9 = 42829 + R(6)

Next, let's divide the quotient, which is 42829, as follows:

385467 ÷ 9 = 42829 + R(6)
42829 ÷ 9 =   4758 + R(7)

Do the same thing with 4758 until the quotient is 0 as follows:

385467 ÷ 9 = 42829 + R(6)
42829 ÷ 9 =   4758 + R(7)

4758 ÷ 9 =     528 + R(6)
528 ÷ 9 =       58 + R(6)
58 ÷ 9 =         6 + R(4)
6 ÷ 9 =         0 + R(6)

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

385467 = 6466769