Which of the following fractions will have a non-terminating recurring decimal expansion?
- $\frac{3}{40}$
- $\frac{7}{125}$
- $\frac{11}{24}$
- $\frac{9}{20}$
Show answer and 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.