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Write the repeating decimal as a fraction.\newline.962962962.962962962

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Full solution

Q. Write the repeating decimal as a fraction.\newline.962962962.962962962
  1. Define xx as decimal: Let xx be the repeating decimal 0.962962962...0.962962962...\newlineWe express this algebraically as:\newlinex=0.962962962...x = 0.962962962...
  2. Multiply by 10001000: To isolate the repeating part, we multiply xx by 10001000, because there are three digits in the repeating sequence (962962).\newline1000x=962.962962…1000x = 962.962962\ldots
  3. Subtract original equation: We subtract the original equation x=0.962962962…x = 0.962962962\ldots from the new equation 1000x=962.962962…1000x = 962.962962\ldots to get rid of the repeating decimals.\newline1000x−x=962.962962…−0.962962962…1000x - x = 962.962962\ldots - 0.962962962\ldots
  4. Perform subtraction: Perform the subtraction on both sides of the equation.\newline1000x−x=9621000x - x = 962\newline999x=962999x = 962
  5. Solve for x: Solve for x by dividing both sides of the equation by 999999. \newlinex=962999x = \frac{962}{999}
  6. Simplify the fraction: Simplify the fraction if possible. In this case, 962962 and 999999 have no common factors other than 11, so the fraction is already in its simplest form.\newlinex=962999x = \frac{962}{999}

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