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explorations in math

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convert the numeral to a numeral in base 10
14
5

  • explorations in math -

    The "1" stands for 5 in base 5.

    145
    =(1*5)+4
    =?

  • explorations in math -

    4.5 + 1.1
    20 + 1

    21

  • explorations in math -

    Your working is for
    415
    =4.5 + 1.1
    =20 + 1
    =21

    The units digit is multiplied by 1, and the second digit from the right is multiplied by the base, 5 in this case.
    If the number has more than 2 digits, the next digits (to the left) are multiplied by the subsequent powers of the base.

    Example:

    3217
    =3*7^2 + 2*7^1 + 1*7^0
    =3*49 + 2*7 + 1*1
    =147 + 14 + 1
    =162

    So
    415
    =4*5^1 + 1*5^0
    =4*5 + 1*1
    =21

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