A rational number can be expressed as a repeating decimal if its denominator (when in simplest form) has prime factors other than only 2 or 5. Let's analyze the given fractions:
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78: This is an integer and can be expressed as a decimal (78.0), which does not repeat.
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5/12: The denominator is 12, which factors to \(2^2 \times 3\). Because it has the factor 3 (not just 2 or 5), it will be a repeating decimal.
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17/25: The denominator is 25, which factors to \(5^2\). Since it only contains the factor 5, this will be a terminating decimal.
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31/40: The denominator is 40, which factors to \(2^3 \times 5\). Since it only contains the factors 2 and 5, this will also be a terminating decimal.
Based on this analysis, the rational number that can be expressed as a repeating decimal is 5/12.