Call this number "x", then write:x = 0.275275275...
1000x = 275.275275275...
Subtract the first equation from the second, and solve for "x". That will give you "x" as a fraction.
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2/111
3 __ 5
7.75 is about 70.5% of 11. 7.75 / 11 = 0.70454545(repeating)
.75 or 75/100
0.375 = 375/1000 = 3/8