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Converting from Base 8 to Base 10 Problems, 2

__Category__: Arithmetic

"Published in Vacaville, California, USA"
Convert 257413_{8} into Base 10.

__Solution__:

The given number which is 257413_{8}_{} is written in Base 8. Base 8 number is also called octal system. The
digits of Base 8 number are 0, 1, 2, 3, 4, 5, 6, and 7.

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 257413_{8} into Base 10. How? Let's multiply each digits by the powers of 8 as follows:

Base 6 Digits: 2 5 7 4 1 3

Multiply by: 8⁵ 8⁴ 8³ 8² 8¹ 8⁰

Add all the digits, we have

(2 x 8⁵) + (5 x 8⁴) + (7 x 8³) + (4 x 8²) + (1 x 8¹) + (3 x 8⁰) = 65536 + 20480 + 3584 + 25 + 8 + 3 = 89636

Therefore, 257413_{8}_{} = **89636 **