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Which decimal is equivalent to 2699\frac{26}{99}?\newlineChoices:\newline(A) 0.2699‾0.\overline{2699}\newline(B) 0.2‾60.\overline{2}6\newline(C) 0.26‾0.\overline{26}\newline(D) 0.26990.2699

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which decimal is equivalent to 2699\frac{26}{99}?\newlineChoices:\newline(A) 0.2699‾0.\overline{2699}\newline(B) 0.2‾60.\overline{2}6\newline(C) 0.26‾0.\overline{26}\newline(D) 0.26990.2699
  1. Convert to decimal: Step 11: Convert the fraction 2699\frac{26}{99} into a decimal by dividing 2626 by 9999.\newlineCalculation: 26÷99≈0.262626262626…26 \div 99 \approx 0.262626262626\ldots
  2. Identify repeating pattern: Step 22: Identify the repeating pattern in the decimal.\newlineObservation: The digits ＂2626＂ repeat.
  3. Match repeating decimal: Step 33: Match the repeating decimal to the given choices.\newlineComparison: The repeating decimal 0.262626…0.262626\ldots matches with choice (C) 0.26‾0.\overline{26}.

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