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Math Help - Repeating decimal help

  1. #1
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    Repeating decimal help

    Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Math Noob View Post
    Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?
    Let x=.208\overline{3}.

    So it follows that 1000x=208.\overline{3} and 10000x=2083.\overline{3}. Now what is 10000x-1000x equal to? From there, see if you can solve for x.

    You may get a ugly looking fraction, but it simplifies nicely. See how far you can go with this.
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  3. #3
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    I would like to see a break down on how and why. Is there a way for you to break this down for me please? I thought when a single digit repeats you only multiply by ten? Then move the decimal towards the right one time then doing the subtracting. I'm confused now lol
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  4. #4
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    Quote Originally Posted by Math Noob View Post
    I would like to see a break down on how and why. Is there a way for you to break this down for me please? I thought when a single digit repeats you only multiply by ten? Then move the decimal towards the right one time then doing the subtracting. I'm confused now lol
    Your number is 0.20833333333333333333.......

    Now read the reply you got again.
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  5. #5
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    I still don't get what your trying to ask me
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  6. #6
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    Quote Originally Posted by Math Noob View Post
    Ok i am stuck in a problem i need some coaching on. This is a repeating decimal, 0.2083 with the last digit 3 repeating i need to form this into a fraction. I don't want the answer but would love to know using the variable x how can i solve this equation?
    What was explained above is this:

    0.20833333333333333333333333...333

    is equivalent to

     \dfrac{2.0833333333333333333333...333}{10}

    & this
     \dfrac{20.833333333333333333333...333}{100}

    & this
     \dfrac{208.3333333333333333333...333}{1000}

    which is also this

     \dfrac{208 + \dfrac{1}{3}}{1000}
    which is also

     \dfrac{ \cfrac{3 \cdot 208 + 1}{3}}{1000}

    and you should be able to reduce that to a simple fraction.
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