0.72 repeating is the sum of a geometric series with first term 0.72 and common factor 1/100. The sum is given by:
(first term) 0.72 0.72 72
--------------------------- = --------------- = ------------ = ------------
1 - common factor 1 - 1/100 99/100 99
This 72/99 can be reduced to 8/11.
0.72 repeating can be rewritten as the fraction 8/11.