3.727272... is equal to 3 + 0.727272...
First, we need to find the common ratio for 0.727272..
For an instance, a = 0.727272...
There are 2 repetitive numbers, seven and two. Multiply the decimal fraction by 100.
(Note: if there is only 1 repetitive number, multiply by 10. if there are 3 repetitive numbers, multiply by 1000 and so on)
100a = 72.727272...
a = 0.727272...
-------------------------- - (substract)
99a = 72
a = [tex] \dfrac{72}{99} [/tex]
a = [tex] \dfrac{8}{11} [/tex]
The common ratio for 0.727272.. is [tex] \dfrac{8}{11} [/tex]
Second, find the common ratio for 3.727272...
3.727272...
= 3 + 0.727272...
= 3 + [tex] \dfrac{8}{11} [/tex]
= [tex] \dfrac{33}{11} + \dfrac{8}{11} [/tex]
= [tex] \dfrac{41}{11}[/tex]
The common ratio for 3.727272.. is [tex] \dfrac{41}{11}[/tex]
