Which statement describes a rational number that has a repeating decimal expansion?

Which statement describes a rational number that has a repeating decimal expansion?

• A. 1/3
• B. 0.25
• C. pi
• D. sqrt(2)

Answer: (A)

Rational numbers can be written as a ratio of integers, and when you write them in decimal form, the expansion either stops or eventually repeats. A repeating decimal means the digits go on forever with a fixed block repeating. One-third equals 0.333..., where the digit 3 repeats indefinitely, so it is a repeating decimal. It is rational because it is a ratio of integers. The other options either terminate in decimal (0.25) or are irrational (pi, sqrt(2)), whose decimals do not repeat. Therefore, the number that is rational and has a repeating decimal expansion is one-third.

Rational numbers can be written as a ratio of integers, and when you write them in decimal form, the expansion either stops or eventually repeats. A repeating decimal means the digits go on forever with a fixed block repeating.

One-third equals 0.333..., where the digit 3 repeats indefinitely, so it is a repeating decimal. It is rational because it is a ratio of integers. The other options either terminate in decimal (0.25) or are irrational (pi, sqrt(2)), whose decimals do not repeat. Therefore, the number that is rational and has a repeating decimal expansion is one-third.