alleryWhich of the following fractions will have a non-terminating recurring decimal expansion?
A$\frac{3}{40}$
B$\frac{7}{125}$
C$\frac{11}{24}$
D$\frac{9}{20}$
Answer & Solution
Correct answer: C. $\frac{11}{24}$
A rational number has a recurring decimal if, in lowest terms, the denominator contains a prime factor other than 2 or 5. Since $24=2^3\times 3$ contains 3, $\frac{11}{24}$ is non-terminating recurring.
The others have denominators made only of 2s and 5s.
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