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When 0.090909.....is converted into a fraction, then the result is
- A1/33
- B1/11
- C2/33
- D6/11
Answer not set
Discussion 1
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CCommunity
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
⇒ 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