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Which decimal is equivalent to 27\frac{2}{7}?\newlineChoices:\newline(A) 0.2857140.285714\newline(B) 0.285714‾0.\overline{285714}\newline(C) 0.27‾0.\overline{27}\newline(D) 0.270.27

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which decimal is equivalent to 27\frac{2}{7}?\newlineChoices:\newline(A) 0.2857140.285714\newline(B) 0.285714‾0.\overline{285714}\newline(C) 0.27‾0.\overline{27}\newline(D) 0.270.27
  1. Calculate Decimal Equivalent: Step 11: Calculate the decimal equivalent of the fraction 27\frac{2}{7} by long division.\newlineDivide 22 by 77. The decimal repeats every six digits as 285714285714.
  2. Compare with Choices: Step 22: Compare the calculated decimal with the given choices.\newlineThe calculated decimal is 0.285714285714…0.285714285714\ldots, which repeats the sequence 285714285714.
  3. Identify Correct Choice: Step 33: Identify the correct choice that matches the repeating decimal. Choice (A) is 0.2857140.285714, which matches the calculated decimal exactly. Choice (B) is 0.285714‾0.\overline{285714}, which also correctly represents the repeating decimal. Choices (C) and (D) do not match the repeating decimal pattern.

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