Hi! I was having trouble with this problem:

I guess this is the easiest way:

.727272727272/.272727272727 = 2.6666666666666667     which is   2 2/3

Here is the long way

let x = .72727272....

  100x = 72.72727272....

100x - x = 99x  = 72       x = 72/99     this is the numerator.....

           now do similar for the denominator....then do the division to get an exact answer.....

denominator = 27/99

72/99  /  27/99   =   72/27 = 24/9= 8/3 = 2 2/3

Neither the decimal ".727272..." nor the decimal ".722222..." can be turned into a fraction.
Also to respond to CPhill's comment I'm pretty sure that he was saying that he needed the answer based on ".72 repeating" not what you assumed he meant. Also the answer you gave can be simplified to

18/25