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Math Help - [SOLVED] Recurring Decimal Help - 0.1575757...

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    [SOLVED] Recurring Decimal Help - 0.1575757...

    I need an explanation of how to do this question

    0.1(57) Where the brackets mark recurring signs.

    I know you start it by saying let x = 0.157575757... just not quite sure where to go from here.
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    Quote Originally Posted by Domoz View Post
    I need an explanation of how to do this question

    0.1(57) Where the brackets mark recurring signs.

    I know you start it by saying let x = 0.157575757... just not quite sure where to go from here.
    Well, if we let x=0.157575757\ldots then 100x=15.757575757\ldots. Now subtract.

    \begin{tabular}{crcr@{.}l}<br />
&$100x$&$=$&15&757575757\ldots\\<br />
$-$&$x$&$=$&0&157575757\ldots\\\hline<br />
&$99x$&=&15&6<br />
\end{tabular}

    So x=\frac{15.6}{99}=\frac{156}{990}=\frac{26}{165}.
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  3. #3
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    Thankyou! I got confused because I got a decimal over a fraction and didn't know what to do.

    Thanks so much!!
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