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Write the repeating decimal as a fraction. \newline.71717171.71717171

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Full solution

Q. Write the repeating decimal as a fraction. \newline.71717171.71717171
  1. Assign xx value: Let xx equal the repeating decimal 0.71717171…0.71717171\ldots\newlinex=0.71717171…x = 0.71717171\ldots
  2. Multiply by 100100: Multiply both sides of the equation by 100100 (since the repeating part is two digits long) to shift the decimal two places to the right.\newline100x=71.71717171…100x = 71.71717171\ldots
  3. Subtract equations: Subtract the original equation x=0.71717171...x = 0.71717171... from the new equation 100x=71.71717171...100x = 71.71717171... to eliminate the repeating decimals.\newline100x−x=71.71717171...−0.71717171...100x - x = 71.71717171... - 0.71717171...
  4. Find value of 99x99x: Perform the subtraction to find the value of 99x99x.99x=7199x = 71
  5. Divide by 9999: Divide both sides of the equation by 9999 to solve for xx.x=7199x = \frac{71}{99}
  6. Check for simplification: Check if the fraction can be simplified. Since 7171 and 9999 have no common factors other than 11, the fraction is already in its simplest form.

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