Math

posted by Hec01

Please help.I need to find two- hundredth digit in the decimal representation of each of the following fractions
5/6
4/11
1/13
Thanks.

  1. Steve

    5/6 = 0.83333...
    4/11 = .363636...
    1/13 = .076923 076923 ...

    Look at the length of each repeating group. Divide that into 200 to see how many repetitions there are, and what remainder.

    For instance

    13/70 = .1857 142857 142857 ...

    There are 4 leading digits, so that leaves 196. The periodic part has length 6. 196/6 = 32 remainder 4.

    So, the 200th digit is
    4 + 32*6 + 4
    The 4th digit of the repeating part is 8. So, the 200th digit is 8.

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