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Can someone explain how you could convert a repeating, nonterminating decimal to a fraction?

Thanks. :)

  • Algebra -

    I will illustrate with an example


    let's just work on the decimal .5676767...
    let x = .5676767...
    multiply by 100 , (because 2 digits repeat, so 2 zeros in 100)
    100x = 56.7676767
    subtract ...
    99x = 56.2
    x = 56.2/99 = 562/990 = 281/495

    so 4.5676767.. = 4 281/495 or 2261/495

    quick way:

    for the numerator,
    --->write down all the digits to the end of the first repeat ---- 567, subtract the non-repeating digits
    567-5 = 562
    for the denominator, for one complete period, we have 1 leading non-repeating followed by 2 repeating ,so
    put down a 9 for each repeating digit (so 2 9's) followed by a 0 for each non-repeating digit, (so one 0)
    or 990

    .567676767... = 562/990 = 281/495

    e.g. .34123123123...
    - (34123 - 34)/99900 = 34089/99900

  • Algebra -

    how are you people

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