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Math Help - decimals

  1. #1
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    decimals

    i want decimal expansion of 1/13 in base 12

    i have tried the "normal" algorithm but i got nowhere
    eg: 1/13 in base 10 is .076923076
    so if i want it in base 12 i go
    .076923076=a/12 + b/144 + c/1728+ . . .
    then mulitiply by the 12
    .923076923=a + b/144 + c/1728 + . .
    this would tell us the first digit after the decimal would be 0 but when i try to repeat the process
    11.07692308 = a + b + c/1728 + . . .
    I dont like that 11 is two decimal spaces.. or is it okay since im in base 12??
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  2. #2
    MHF Contributor chiph588@'s Avatar
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     11 is correct! you just need to remember that we set  10 = A , \; 11 = B ... to give one digit representations.
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    By those three steps you wrote out, you should see you get a repeating fraction here.

     \frac{1}{13} = .0B0B0B0B0B..._{12}
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  4. #4
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    Thanks
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    An alternate method

    I like to write:
    1 = 0.9999999...
    in base 10.

    So I get 1/11 by dividing the RHS by 11 to get
    1/11 = 0.0909090909 etc.

    In the same fashion, for base B+1
    1 = 0.BBBBBBBB
    So 1/(11 in base B+1)
    1 = 0.0B0B0B....
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  5. #5
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    okay i think i get it except im still not sure how im actually supposed to write it .. would my final answer be 1/13=0b0b0b0b.. or do i subsititute b in??
    I get that its a repeating decimal since the order is 2.
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  6. #6
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    im working on a similar problem 1/14 base 12

    the period is 10.

    would i do this the same way?
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