# Math

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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 -

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 2526
= 2*6² + 5*6¹ + 2*6^0
= 72 + 30 + 2
= 10410

To convert 10210 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 10210 = 4045

• Math -

Thanks. How did it change from 104 base 10 to 102?

• Math -

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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