SOLUTION: Evaluate the decimal expansion below as a ratio of integers expressed in lowest terms. .23232323232323... Thank you kindly.

Algebra ->  Sequences-and-series -> SOLUTION: Evaluate the decimal expansion below as a ratio of integers expressed in lowest terms. .23232323232323... Thank you kindly.      Log On


   

Question 986529: Evaluate the decimal expansion below as a ratio of integers expressed in lowest terms.
.23232323232323...
Thank you kindly.
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!

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%2F99            <-- answer 


Edwin