Which of the following rational numbers are terminating decimals?

Key insight: A rational number in lowest terms has a terminating decimal expansion if and only if its denominator has no prime factors other than 2 and 5.

• 17 / (2⁴ × 5²): The denominator's prime factors are only 2 and 5, so this fraction is a terminating decimal.

• 125 / (3³ × 7²): The denominator contains primes 3 and 7. Since these are not 2 or 5, the decimal expansion is not terminating.

• 68 / (2² × 5² × 7²): Cancel the common 2² factor in numerator and denominator to get 17 / (5² × 7²). The denominator still has 7, so the decimal expansion is not terminating.

• 25 / (3² × 2³): The denominator includes a factor 3, which is neither 2 nor 5, so the decimal expansion is not terminating.

Conclusion: Of the given fractions, only 17 / (2⁴ × 5²) is a terminating decimal.