Which of the following rational numbers can be expressed as a repeating decimal: 7/8 , 5/12 , 17/25 , or 31/40 ?(1 point)
To determine if a rational number can be expressed as a repeating decimal, we need to express it as a fraction in the form $\frac{a}{b}$, where $b$ only contains the prime factors 2 and 5.
From the given options,
- $\frac{7}{8}$ cannot be expressed as a repeating decimal because 8 contains a prime factor of 2.
- $\frac{5}{12}$ cannot be expressed as a repeating decimal because 12 contains a prime factor of 2.
- $\frac{17}{25}$ can be expressed as a repeating decimal because 25 only contains the prime factors 5, which is suitable for a repeating decimal.
- $\frac{31}{40}$ cannot be expressed as a repeating decimal because 40 contains a prime factor of 2.
Therefore, only $\boxed{\frac{17}{25}}$ can be expressed as a repeating decimal.