SOLUTION: How do you write the repeating decimal 0.2424.... as a quotient of integers?

 N = 0.24242424242424....

Now since there are 2 digits that repeat multiply both sides 
by  or 100

100N = 24.242424242424....

Now write the first equation underneath the second equation,
linng up the decimal points:

100N = 24.242424242424....
   N =  0.24242424242424....

Now subtract:

100N = 24.242424242424....
   N =  0.24242424242424....
----------------------------
 99N = 24.00000000000000...

So you see the decimals all cancel out

 99N = 24

Divide both sides by 99



Now simplify and reduce the fraction:

 

Check by dividing 8 by 33 and the get 0.2424242424...

A short cut is to put the repeating digits over a number
that has that many 9's as its only digits and reduce if possible.

For example, to change this to a quotient of integers:

0.972972972972...

Put 972 over 999

 reduce the fraction to 

Edwin