Posted by **Heather** on Wednesday, June 30, 2010 at 9:03pm.

How do you convert a number to whatever base it indicates? For example: convert 252 base six to base five. I have tried posting for my teacher to help me, but he doesn't seem to get what I am asking. Can someone please explain the process and not just the answer? Thanks!!

- Math -
**MathMate**, Thursday, July 1, 2010 at 10:44am
Most of the time, you would convert numbers from "foreign" bases to base 10, then convert to the target base by division.

From a number in base n, we recognize that each digit from the right represents n^x, where x is the position from the right.

So 252_{6}

= 2*6² + 5*6¹ + 2*6^0

= 72 + 30 + 2

= 104_{10}

To convert 102_{10} to base 5, we divide by 5 successively and collect the remainders as digits from the right.

102/5=20R4

20/5=4R0

4/5=0R4

So 102_{10} = 404_{5}

- Math -
**Heather**, Thursday, July 1, 2010 at 3:09pm
Thanks. How did it change from 104 base 10 to 102?

- Math -
**DENISE**, Monday, May 9, 2011 at 11:39pm
102ten to base 5 is not 404five it is 402five

102/5=20 r 2

20/5=4 r 0

4/5 =0 r 4

so that gives you 402five

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