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Need help recuuring decimals

  1. Feb 3, 2010 #1
    need help!! recuuring decimals

    hey, I'm in yr 11 advanced maths and I'm on a section in my book, where I'm converting recurring decimals to common fractions. i have a series of questions, after i finished the first couple i cheeked the back of the book to make sure I did them correctly but the book says they are all wrong. hears what i did and the books answer after it. p.s. the last digit is the only recurring decimal eg 4 out of .34...

    .34...... .57......
    x=.34...... x=.57.....
    10x=3.4..... 10x=5.7.......
    100x=34.4..... 100x=57.7.......
    100x-10x=34 90x=57
    x=34/90 x=57/90
    x=17/45 x=19/30

    book answer
    31/90 38/90
    Last edited by a moderator: Feb 3, 2010
  2. jcsd
  3. Feb 3, 2010 #2
    Re: need help!! recuuring decimals

    For instance, in the first case, if x = 0.344444(etc); 10x = 3.44444(etc); 100x = 34.444444(etc) , so what does 34.444444(etc) - 3.44444(etc) equal?
  4. Feb 3, 2010 #3


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    Re: need help!! recuuring decimals

    No, it should be 100x 10x= 34.4...-3.4.... so 90x= 31, not 34.

    Similarly, subtracting 10x= 5.7.... from 100x= 57.7.... gives 90x= 57.7.... - 5.7... or 90x= 52, not 57.

  5. Feb 4, 2010 #4
    Re: need help!! recuuring decimals

    thanks for the help! XD
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