alleryWhich fraction has a TERMINATING decimal expansion?
A$\frac{7}{40}$
B$\frac{4}{15}$
C$\frac{1}{14}$
D$\frac{5}{21}$
Answer & Solution
Correct answer: A. $\frac{7}{40}$
A p/q in lowest form terminates iff q's prime factors are only 2's and/or 5's.
40 = 2³ × 5 (only 2 and 5) → terminates.
15 = 3 × 5, 14 = 2 × 7, 21 = 3 × 7 (all contain primes other than 2 or 5) → recurring.
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