# Recurring decimals and sources needed

• Jan 5th 2010, 08:06 AM
Mukilab
Recurring decimals and sources needed
Show that the recurring decimal $\displaystyle 0.\overline{69}$ can be written as the fraction $\displaystyle \frac{23}{33}$

$\displaystyle \mbox{I showed that}\frac{2}{3}=0.6\mbox{and that}\frac{3}{33}=0.09\mbox{is this a correct explanation?}$

Also can anyone direct me to any good sources to learn how to create cumulative frequency columns when faced with inequalities adn how to draw box plots.
• Jan 5th 2010, 08:24 AM
earboth
Quote:

Originally Posted by Mukilab
Show that the recurring decimal $\displaystyle 0.\overline{69}$ can be written as the fraction $\displaystyle \frac{23}{33}$

...

Let

$\displaystyle x = 0.\overline{69}$

Then

$\displaystyle 100x= 69.\overline{69}$

Now subtract:

$\displaystyle 99x = 69~\implies~x=\frac{69}{99}=\frac{23}{99}$
• Jan 5th 2010, 08:32 AM
Mukilab
Quote:

Originally Posted by earboth
Let

$\displaystyle x = 0.\overline{69}$

Then

$\displaystyle 100x= 69.\overline{69}$

Now subtract:

$\displaystyle 99x = 69~\implies~x=\frac{69}{99}=\frac{23}{99}$

Wow amazing method, thank you!