# Recurring decimals and sources needed

• January 5th 2010, 09:06 AM
Mukilab
Recurring decimals and sources needed
Show that the recurring decimal $0.\overline{69}$ can be written as the fraction $\frac{23}{33}$

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

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.
• January 5th 2010, 09:24 AM
earboth
Quote:

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

...

Let

$x = 0.\overline{69}$

Then

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

Now subtract:

$99x = 69~\implies~x=\frac{69}{99}=\frac{23}{99}$
• January 5th 2010, 09:32 AM
Mukilab
Quote:

Originally Posted by earboth
Let

$x = 0.\overline{69}$

Then

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

Now subtract:

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

Wow amazing method, thank you!