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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- Mar 7th 2009, 07:14 PMDomoz[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. - Mar 7th 2009, 07:55 PMReckoner
Well, if we let $\displaystyle x=0.157575757\ldots$ then $\displaystyle 100x=15.757575757\ldots.$ Now subtract.

$\displaystyle \begin{tabular}{crcr@{.}l}

&$100x$&$=$&15&757575757\ldots\\

$-$&$x$&$=$&0&157575757\ldots\\\hline

&$99x$&=&15&6

\end{tabular}$

So $\displaystyle x=\frac{15.6}{99}=\frac{156}{990}=\frac{26}{165}.$ - Mar 7th 2009, 07:57 PMDomoz
Thankyou! I got confused because I got a decimal over a fraction and didn't know what to do.

Thanks so much!!