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Math Help - Converting Decimals to Fractions

  1. #1
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    Converting Decimals to Fractions

    1/34 to decimal=


    Change to Fraction
    x=.12361236


    Changes to Fraction
    x=.352171717


    Please help

    Thanks,

    Steve
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  2. #2
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by skweres1 View Post
    Change to Fraction
    x=.12361236
    For a repeating fraction take the part that repeats and put the same number of 9s as the denominator and cancel if appropriate.

    x = \frac{1236}{9999} = \frac{412}{3333}
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  3. #3
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    Quote Originally Posted by skweres1 View Post
    1/34 to decimal=
    Change to Fraction
    x=.12361236
    Changes to Fraction
    x=.352171717
    Please help
    Thanks,
    Steve
    x = 0.352171717
    This is a repeating decimal:
    Take it apart

    0.352 + 0.000171717 = 0.352171717

    as e^(i*pi) showed in his post:
    \dfrac{17}{99000} = 0.0001717171717171717...


    \dfrac{352}{1000} + \dfrac{17}{99000} = 0.352171717

    you can see that 352/1000 can be reduced
    \dfrac{352}{1000} = \dfrac{176}{500} = \dfrac{88}{250} = \dfrac{44}{125}

    so add the fractions
    \dfrac{44}{125} + \dfrac{17}{99000}

    need a common denominator
    \dfrac{44}{125} \times \dfrac{99000}{99000} \,+\, \dfrac{17}{99000}\times \dfrac{125}{125}

    \dfrac{ 44 \cdot 99000 \, + \, 17 \cdot 125 }{ 125 \cdot 99000}

    \dfrac{ 4356000 \, + \, 2125 }{ 12375000}

    \dfrac{ 4358125 }{ 12375000}
    and that can be reduced:

    divide numerator & denominator by 625 to get the fraction in lowest terms.

    Spoiler:
    \dfrac{6973}{19800}


    The continued fraction algorithm is the method of choice for doing this type of conversions.
    The above is not that algorithm.
    Perhaps someone will explain/demonstrate the continued fraction algorithm for converting decimals to rationals.
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  4. #4
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    if the digits are recurring indefinitely

    x= 0.12361236...

    10000x=1236.12361236...
    -
    x= 0.12361236...

    9999x=1236

    x=\frac{1236}{9999}


    if the fraction doesnt repeat indefinitely

    0.12361236=\frac{12361236}{100000000}
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  5. #5
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    Hello, Steve!

    I will assume those are repeating decimals.


    \frac{1}{34}\text{ to decimal}

    Just divide it out until you get a repeating cycle . . .

    \frac{1}{34} \;=\;0.0 \overline{2941176970588235}\, \hdots




    \text{Change to fraction: }\:x \:=\:0.12361236\hdots

    \begin{array}{ccccc}\text{Multiply by 10,000:} & 10,000x &=& 1236.12361236\hdots \\<br />
\text{Subtract }x\!: & \qquad\;\; x &=& \quad\;\; 0.12361236\hdots \\<br />
\text{and we have:} & \;9999x &=& 1236\qquad\qquad\quad\;\; \end{array}<br />

    Therefore: . x \;=\;\frac{1236}{9999} \;=\;\frac{412}{3333}




    \text{Change to fraction: }\:x \:=\:0.362171717\hdots

    \begin{array}{ccccc}\text{Multiply by 100,000:} & 100,\!000x &=& 36217.171717\hdots \\<br />
\text{Multily by 1,000:} & \;\;\;1,\!000x &=& \quad 362.171717\hdots \\<br />
\text{Subtract:} & \;99,\!000x &=& 35855\qquad\qquad\;\;<br />
\end{array}

    Therefore: . x \;=\;\frac{35,\!855}{99,\!000} \;=\;\frac{7,\!171}{19,\!800}

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