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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.
    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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