Question
Which one of the following is a correct statement?
(a) Decimal expansion of a rational number is terminating
(b) Decimal expansion of a rational number is non-terminating
(c) Decimal expansion of an irrational number is terminating
(d) Decimal expansion of an irrational number is non-terminating and non-repeating
Solution
Option (a)
✘ Incorrect
A rational number can be either terminating or non-terminating repeating.
Option (b)
✘ Incorrect
Not all rational numbers are non-terminating.
Option (c)
✘ Incorrect
Irrational numbers are never terminating.
Option (d)
✔ Correct
The decimal expansion of an irrational number is always non-terminating and non-repeating.
Final Answer
✔ Correct option: (d)