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

• 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.

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

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!!