## Tuesday, August 4, 2015

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

Category: Arithmetic

"Published in Vacaville, California, USA"

Convert 5120357 into Base 10.

Solution:

The given number which is
5120357 is written in Base 7. Base 7 number is also called heptimal system. The digits of Base 7 number are 0, 1, 2, 3, 4, 5, and 6.

On the other hand, Base 10 number is a number whose digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. 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. Base 10 number is a common number that we are using right now in everyday life.

Now, let's convert
5120357 into Base 10. How? Let's multiply each digits by the powers of 7 as follows:

Base 6 Digits:        5      1      2
0      3      5
Multiply by:            7
⁵     7⁴     7³
7²     7¹     7⁰

Add all the digits, we have

(5 x
7⁵) + (1 x 7) + (2 x 7³) + (0 x ) + (3 x ) + (5 x 7⁰) = 84035 + 2401 + 686 + 0 + 21 + 5 = 87148

Therefore,
5120357 = 87148