Which of the following numbers will have a terminating decimal value?
\(\frac{9}{45}\)
Step 1 — A fraction in lowest terms has a terminating decimal iff its denominator's prime factors are only 2 and/or 5.
Step 2 — Reduce each: \(\dfrac{6}{45} = \dfrac{2}{15},\ \dfrac{12}{45} = \dfrac{4}{15},\ \dfrac{9}{45} = \dfrac{1}{5},\ \dfrac{3}{45} = \dfrac{1}{15}\).
Step 3 — Only \(\dfrac{1}{5}\) has denominator with prime factor 5 alone, so only \(\dfrac{9}{45}\) terminates (\(= 0.2\)).
Hence, \(\dfrac{9}{45}\).
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