__Category__: Arithmetic"Published in Vacaville, California, USA"

Convert A245A3B

_{12}into Base 10.

__Solution__:

The given number which is A245A3B

_{12}is written in Base 12. Base 12 number is also called duodecimal system. The digits of Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. Since 10 and 11 are not accepted as a digit, then we have to substitute a variable which is A = 10 and B = 11. Hence, the digits of a Base 12 number are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, and B.

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 A245A3B

_{12}into Base 10. How? Let's multiply each digits by the powers of 12 as follows:

Base 6 Digits: A 2 4 5 A 3 B

Multiply by: 12⁶ 12⁵ 12⁴ 12³ 12² 12¹ 12⁰

Add all the digits, we have

(A x 12⁶) + (2 x 12⁵) + (4 x 12⁴) + (5 x 12³) + (A x 12²) + (3 x 12¹) + (B x 12⁰) = 29859840 + 497664 + 82944 + 8640 + 1440 + 36 + 11 = 30450575

Therefore, A245A3B

_{12}=

**30450575**