2018 · Q5
Which one of the following is correct?
Elementary MathematicsNumber System
- ADecimal expansion of a rational number is terminating.
- BDecimal expansion of a rational number is non-terminating.
- CDecimal expansion of an irrational number is terminating.
- DDecimal expansion of an irrational number is non-terminating and non-repeating.
Explanation
A rational number's decimal expansion always terminates or eventually repeats, so options (A) and (B), stated absolutely, are both false. An irrational number's expansion never terminates and never settles into a repeating block — exactly what option (D) states. The keyed answer is (D).