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Math Help - Recurring decimals and sources needed

  1. #1
    Senior Member Mukilab's Avatar
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    Recurring decimals and sources needed

    Show that the recurring decimal 0.\overline{69} can be written as the fraction \frac{23}{33}

    \mbox{I showed that}\frac{2}{3}=0.6\mbox{and that}\frac{3}{33}=0.09\mbox{is this a correct explanation?}

    Also can anyone direct me to any good sources to learn how to create cumulative frequency columns when faced with inequalities adn how to draw box plots.
    Last edited by Chris L T521; January 5th 2010 at 10:56 AM. Reason: fixed LaTeX
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  2. #2
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    earboth's Avatar
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    Quote Originally Posted by Mukilab View Post
    Show that the recurring decimal 0.\overline{69} can be written as the fraction \frac{23}{33}

    ...
    Let

    x = 0.\overline{69}

    Then

    100x= 69.\overline{69}

    Now subtract:

    99x = 69~\implies~x=\frac{69}{99}=\frac{23}{99}
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  3. #3
    Senior Member Mukilab's Avatar
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    Quote Originally Posted by earboth View Post
    Let

    x = 0.\overline{69}

    Then

    100x= 69.\overline{69}

    Now subtract:

    99x = 69~\implies~x=\frac{69}{99}=\frac{23}{99}

    Wow amazing method, thank you!
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