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Homework Help: Converting recurring decimal to a fraction

  1. Apr 2, 2009 #1
    3.741 (41 is recurring)

    answer is 1852/495

    but ii don't know how to work it out

    thanks :)
  2. jcsd
  3. Apr 2, 2009 #2


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    Science Advisor

    3.74141414141... = 3.7 + 1.0101010101010... * 0.041

    Can you figure out a fraction for 1.01010101010?

    If so, you can proceed from there.
  4. Apr 2, 2009 #3
    You could also try assigning the number to a variable, for example

    n = 3.741414141...

    If we multiply both sides of the above equation by 10, we have

    10n = 37.41414141...

    Try multiplying the original equation by another number, so that it might be possible to get rid of the repeating decimal part of the number by performing some arithmetic operation on two of the equations...
  5. Apr 2, 2009 #4


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    Homework Helper

    Use the geometric series formula or, if you don't know what that is, do it algebraically as so:

    To convert 0.52222... into a fraction

    let x=0.52222... (1)
    10x=5.22222... (2)
    (2) - (1)
    9x = 5.2222...-0.5222 = 4.7
    Therefore x = 4.7/9 = 47/90

    Try apply this idea to your question.
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