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How do you write 0.1‾0.\overline{1} as a fraction?\newlineChoices:\newline(A) 16\frac{1}{6}\newline(B) 18\frac{1}{8}\newline(C) 19\frac{1}{9}\newline(D) 13\frac{1}{3}

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Evaluate definite integrals using the chain ruleright chevron icon

Full solution

Q. How do you write 0.1‾0.\overline{1} as a fraction?\newlineChoices:\newline(A) 16\frac{1}{6}\newline(B) 18\frac{1}{8}\newline(C) 19\frac{1}{9}\newline(D) 13\frac{1}{3}
  1. Convert to Fraction: Convert the repeating decimal to a fraction using the formula for infinite repeating decimals. Let x=0.1‾x = 0.\overline{1}.
  2. Set up Equation: Set up the equation based on the repeating decimal. Multiply xx by 1010 to shift the decimal point.
  3. Subtract and Eliminate: Subtract the original xx from 10x10x to eliminate the repeating part.
  4. Solve for xx: Solve for xx by dividing both sides by 99.

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