[SOLVED] Recurring Decimal Help - 0.1575757...

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March 7th 2009, 07:14 PM
Domoz

[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.
March 7th 2009, 07:55 PM
Reckoner

Quote:

Originally Posted by Domoz

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 $x=\frac{15.6}{99}=\frac{156}{990}=\frac{26}{165}.$
March 7th 2009, 07:57 PM
Domoz

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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