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Which decimal is equivalent to 59\frac{5}{9}?\newlineChoices:\newline(A) 0.5‾0.\overline{5}\newline(B) 0.9‾0.\overline{9}\newline(C) 0.18‾0.1\overline{8}\newline(D) 0.18‾0.\overline{18}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which decimal is equivalent to 59\frac{5}{9}?\newlineChoices:\newline(A) 0.5‾0.\overline{5}\newline(B) 0.9‾0.\overline{9}\newline(C) 0.18‾0.1\overline{8}\newline(D) 0.18‾0.\overline{18}
  1. Convert to Decimal: Step 11: Convert the fraction 59\frac{5}{9} into a decimal by dividing 55 by 99.\newlineCalculation: 5÷9=0.55555…5 \div 9 = 0.55555\ldots (repeating decimal).
  2. Identify Repeating Sequence: Step 22: Identify the repeating sequence in the decimal.\newlineObservation: The digit '55' repeats indefinitely.
  3. Match to Choices: Step 33: Match the repeating decimal to the given choices.\newlineComparison: The repeating decimal 0.55555…0.55555\ldots matches with choice (A)0.5‾(A) 0.\overline{5}.

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