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Which decimal is equivalent to 17\frac{1}{7}?\newlineChoices:\newline(A) 0.17‾0.\overline{17}\newline(B) 0.170.17\newline(C) 0.1428570.142857\newline(D) 0.142857‾0.\overline{142857}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. Which decimal is equivalent to 17\frac{1}{7}?\newlineChoices:\newline(A) 0.17‾0.\overline{17}\newline(B) 0.170.17\newline(C) 0.1428570.142857\newline(D) 0.142857‾0.\overline{142857}
  1. Calculate Decimal Equivalent: Step 11: Calculate 11 divided by 77 using long division to find the decimal equivalent.\newline11 divided by 77 equals approximately 0.1428570.142857 repeating. This is a repeating decimal, which means the same digits repeat indefinitely.
  2. Compare with Choices: Step 22: Compare the result from Step 11 with the given choices. The calculated decimal 0.1428570.142857 matches with choice (C) 0.1428570.142857 and (D) 0.142857‾0.\overline{142857}, which indicates a repeating decimal pattern.
  3. Correct Notation for Repeating Decimals: Step 33: Determine the correct notation for repeating decimals among the choices.\newlineChoice (D) 0.142857‾0.\overline{142857} correctly represents the repeating nature of the decimal, whereas choice (C) is just the decimal without indicating repetition.

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