## Saturday, August 1, 2015

### Converting from Base 10 to Base 7 Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 306 into Base 7.

Solution:

The given number which is 306
is written in Base 10. 306 can also be written as 30610. 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
306 into Base 7. How? Let's divide 306 by 7 as follows:

306 ÷ 7 = 43 + R(5)

Next, let's divide the quotient, which is 43, as follows:

306 ÷ 7 = 43 + R(5)
43 ÷ 7 =   6 + R(1)

Do the same thing with 6 until the quotient is 0 as follows:

306 ÷ 7 = 43 + R(5)
43 ÷ 7 =   6 + R(1)

6 ÷ 7 =   0 + R(6)

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

306
= 6157