Which of the following has a terminating decimal expansion?

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KollegeApply · Accepted Answer

bb($\frac{19}{80}$) Explanation: A rational number p/q in lowest terms has a terminating decimal expansion exactly when q’s prime factors are only 2 and/or 5 (q = 2m $\times$ 5n). Check the options (already in simplest form): $\frac{32}{91}$, denominator 91 = 7 $\times$ 13 (contains primes other than 2 or 5) $\to$ nonterminating. $\frac{19}{80}$, denominator 80 = 24 $\times$ 5 $\to$ terminating. (correct) $\frac{23}{45}$, denominator 45 = 32 $\times$ 5 (contains 3) $\to$ nonterminating. $\frac{25}{42}$, denominator 42 = 2 $\times$ 3 $\times$ 7 (contains 3 and 7) $\to$ nonterminating.

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