DRDO Multi tasking staff Model paper 9

Given:
We have to convert 0.090909..... into a fraction.
Calculations:
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