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Math Help - P/q?

  1. #1
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    P/q?

    The problem states:
    Express 5.2727... as a rational number in the form of p/q where p and q are positive integers with no common factors.
    The only way I know how to solve is to keep plugging number in the calculator until I find that number...I found the answer to be 61 for p and 11 for q, but I don't actually know how to do it.

    Can you explain this to me?
    Last edited by Bracketology; November 13th 2010 at 09:31 PM.
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  2. #2
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    Quote Originally Posted by Bracketology View Post
    The problem states:
    Express 5.2727... as a rational number in the form of p/q where p and q are positive integers with no common factors.
    The only way I know how to solve is to keep plugging number in the calculator until I find that number...I found the answer to be 61 for p and 11 for q, but I don't actually know how to do it.

    Can you explain this to me?
    Let x denote the number 5.\overline{27}

    Then

    \begin{array}{rcr}100x&=&527.\overline{27} \\ x&=&5.\overline{27}\end{array}

    Subtract columnwise and you'll get:

    99x = 522~\implies~x=\dfrac{522}{99}=\dfrac{58}{11}

    Btw: \dfrac{61}{11} = 5.\overline{54}
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  3. #3
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    oops, should have said 58/11. Yea, I got the answer in the calculator. Thanks for the help.
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