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The decimal expansion of a rational number $\frac{a}{b}$ will terminate if, after reducing it to lowest terms, the prime factorisation of $b$ is
Aonly of the form $2^n5^m$
Bonly of the form $3^n5^m$
Conly of the form $2^n3^m$
Dany product of prime numbers
Answer & Solution
Correct answer: A. only of the form $2^n5^m$
A rational number in lowest terms has a terminating decimal expansion exactly when the denominator has no prime factors other than 2 and 5. So $b$ must be of the form $2^n5^m$.
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