The answer depends on what string is repeating. It is not clear from the question whether the recurring fraction is meant to be 0.131313... or 0.133333...
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If you mean: 0.151515.....repeating then as a fraction it is 5/33
0.13333333 repeating in fraction = 12/90 or 2/15
It is: 53/99It is: 0.5333 ... repeating = 8/15 as a fraction
The fraction of the repeating decimal 0.7... is 7/9
If both digits are repeating then as a fraction it is 37/99