Question 986529
<pre>

Write N = in front of it.

N = .23232323232323...

Since there are 2 repeating digits multiply both sides by 10² or 100

100N = 23.232323232323

Now under that write the original equation, lining up the decimals 

100N = 23.232323232323...
   N =   .23232323232323...


Then subtract the equations.  The repeating decimals cancel.

100N = 23.232323232323...
   N =   .23232323232323...
---------------------------
 99N = 23.00000000000000...   <-- ignore the 0's
 99N = 23
   N = {{{23/99}}}            <-- answer 


Edwin</pre>