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