Question
The decimal expansion of a rational number is:
(a) terminating or non-terminating non-repeating
(b) terminating or non-terminating repeating
(c) terminating and repeating
(d) none of these
Solution
A rational number can be written in the form \( \frac{p}{q} \), where \( q \neq 0 \).
Its decimal expansion is always either:
- Terminating (finite number of digits)
- Non-terminating but repeating (recurring pattern)
Examples:
\[ \frac{1}{2} = 0.5 \quad \text{(terminating)} \]
\[ \frac{1}{3} = 0.333\ldots \quad \text{(non-terminating repeating)} \]
It can never be non-terminating and non-repeating (that is irrational).
Final Answer
✔ Correct option: (b) terminating or non-terminating repeating