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How do you write 0.1‾0.\overline{1} as a fraction?\newlineChoices:\newline(A) 19\frac{1}{9}\newline(B) 18\frac{1}{8}\newline(C) 13\frac{1}{3}\newline(D) 14\frac{1}{4}

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Convert between repeating decimals and fractionsright chevron icon

Full solution

Q. How do you write 0.1‾0.\overline{1} as a fraction?\newlineChoices:\newline(A) 19\frac{1}{9}\newline(B) 18\frac{1}{8}\newline(C) 13\frac{1}{3}\newline(D) 14\frac{1}{4}
  1. Recognize decimal pattern: Recognize the repeating decimal. 0.ar{1} means 0.1111...0.1111...
  2. Shift decimal point: Let x=0.1111…x = 0.1111\ldots Multiply both sides by 1010 to shift the decimal point. 10x=1.1111…10x = 1.1111\ldots
  3. Subtract and simplify: Subtract the original xx from 10x10x. 10x−x=1.1111...−0.1111...10x - x = 1.1111... - 0.1111... This gives 9x=19x = 1
  4. Solve for x: Solve for x by dividing both sides by 99. x=19x = \frac{1}{9}

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