# Thread: Recurring decimals and sources needed

1. ## 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.

2. 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:

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

3. 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!