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Math Help - Explain how 4/15 is equivalent to recurring decimal.

  1. #1
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    Explain how 4/15 is equivalent to recurring decimal.

    As stated in the title -
    Explain how 4/15 is equivalent to recurring decimal.
    Many Thaanks!
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by BabyMilo View Post
    As stated in the title - Many Thaanks!
    Hi BabyMilo,

    Let's do the long division on this thing.

    Code:
     
         0  .  2   6   6    6   6
         ------------------------
    15 | 4  .  0   0   0    0   0 
         0
        ----------
         4     0
         3     0
         ---------
          1    0   0
               9   0
          -----------
               1   0   0
                   9   0
                 ----------
                   1   0
    As you can see, the 6 will continue to repeat because the remainder will always be 10 as we continue to divide.

    \frac{4}{15}=0.2\overline{6}
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  3. #3
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    no other mathematical ways? Thanks anyway!
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  4. #4
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    Sure there is.

    Let S = 0.266\overline{6}.

    Multiply both sides by 100: 100S = 26.66\overline{6}

    Subtract by the first line: 99S = 26.400..

    So: S = \frac{26.4}{99} \cdot \underbrace{{\color{red}\frac{5}{5}}}_{\displaysty  le =1} = \frac{132}{495}

    Reduce the final fraction and you'll get what you want.
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