Which of the following fractions, when expanded, would lead to a decimal value that re-occurs most late?

Answer Choices

Correct answer marked below

\frac{12}{700}

\frac{991}{172}

Correct

\frac{257}{187}

\frac{122}{390}

\frac{937}{570}

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Explanation

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Official Explanation

Official

The answer is B.

Repeating digits are given by prime numbers other than 2 or 5 in the denominator. The larger the prime number in the denominator, the more likely it is for that fraction to have a decimal value that re-occurs most late.

So among the options:

- A:

700 = 2^2 \cdot 5^2 \cdot 7

→ remaining factor = 7

- B:

172 = 2^2 \cdot 43

→ remaining factor = 43 (large prime): This looks immediately suspicious as the likely winner because 43 is big and prime.…

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What this question tests

What it tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Common trap

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.