[SOLVED] Recurring Decimal Help - 0.1575757...

• Mar 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.
• Mar 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 $\displaystyle x=0.157575757\ldots$ 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 PM
Domoz
Thankyou! I got confused because I got a decimal over a fraction and didn't know what to do.

Thanks so much!!