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Math Help - Express Using Fractions

  1. #1
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    Express Using Fractions

    Express the following repeating decimals as fractions.

    (1) 13.513513...

    (2) 52.31272727...
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  2. #2
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    Quote Originally Posted by sologuitar View Post
    Express the following repeating decimals as fractions.

    (1) 13.513513...

    (2) 52.31272727...
    1) S = 13.513513 ... (A)

    1000S = 13513.513 ... (B)

    (B) - (A): ...... Now solve for S.


    2) S = 52.31272727 .... (A)

    100S = 5231.272727 .... (B)

    10000S = 523127.2727 .... (C)

    (C) - (B): .... Now solve for S.
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  3. #3
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    Quote Originally Posted by sologuitar View Post
    Express the following repeating decimals as fractions.

    (1) 13.513513...

    (2) 52.31272727...
    Note that

    13.513513...=13+\frac{513}{1,000}+\frac{513}{1,000  ,000}+...

    the second problem is similar..
    Last edited by VonNemo19; December 3rd 2009 at 05:38 PM.
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  4. #4
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    How???

    Quote Originally Posted by mr fantastic View Post
    1) S = 13.513513 ... (A)

    1000S = 13513.513 ... (B)

    (B) - (A): ...... Now solve for S.


    2) S = 52.31272727 .... (A)

    100S = 5231.272727 .... (B)

    10000S = 523127.2727 .... (C)

    (C) - (B): .... Now solve for S.
    I can do it now. However, where did S come from? What about this type of question indicated that subtraction was needed to find the answer?
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    Where???

    Quote Originally Posted by VonNemo19 View Post
    Note that

    13.513513...=13+\frac{513}{1,000}+\frac{513}{1,000  ,000}+...

    the second problem is similar..
    Thanks for your reply but where are you going with the fractions?
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  6. #6
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    Quote Originally Posted by sologuitar View Post
    I can do it now. However, where did S come from? What about this type of question indicated that subtraction was needed to find the answer?
    S is the symbol I used to represent the unknown fraction.

    1) (B) - (A): 999S = 13500 => S = 13500/999 = 500/37.
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  7. #7
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    Got it...

    Quote Originally Posted by mr fantastic View Post
    S is the symbol I used to represent the unknown fraction.

    1) (B) - (A): 999S = 13500 => S = 13500/999 = 500/37.
    Thanks. I can use any variable other than S, right?
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  8. #8
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    Quote Originally Posted by sologuitar View Post
    Thanks. I can any variable other than S, right?
    Yes. Use x if you like ....
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