When 0.090909.....is converted into a fraction, then the result is

Let 0.090909…. = x
0.0909090 is the given decimal number
Here, 09 is repeated i.e., 2 digits are repeating
Multiply the decimal by 102 i.e., 10 to the power of repeating digits
9.090909
9.090909… = 9 + 0.090909
100x = 9 + x
99x = 9
x = 9/99 = 1/11
The fraction is 1/11

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