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Math Help - decimal expansion

  1. #1
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    decimal expansion

    This is the problem, just wanting some help with it AND an explanation

    There is a rule for the decmal expansion of 1/m, regardless of whether m is prime or not:

    the number of digits in the repetenddivides the number of integers from 1 to m whose highest common factor with m is 1.

    For example 1/21 = 0.047619 (recurring), the number of digits in the repetend is 6, and there are 12 integers from 1 to 21, whose highest common factor with 21 is 1: 1,2,4,5,8,10,11,13,16,17,19,20.

    a) Check this rule for 1/51

    b) find the family of fractions amongst n/51 for n = 1,2,3...,50, that have the same digits in their repetends as 1/51 but cyclically rotated.

    c) Check the rule for all other families of fractions amongst n/51 for n = 1,2,3,...,50, that have the same digits in their repetends but cyclically rotated.

    sry if this sounds a bit rude or something, but when you answer can you please put it in with working, and why, so i actually know how to do it...

    Big thanks to whoever helps!
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  2. #2
    Super Member Matt Westwood's Avatar
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    I replied to this in the original thread, sorry, that was at the same time you were trying to re-post it and move it.
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  3. #3
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    Maybe this helps.
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