Question
Statement-1 (Assertion): The decimal representation of \( \frac{3}{8} \) is terminating.
Statement-2 (Reason): If the denominator of a rational number is of the form \(2^m \times 5^n\), where \(m, n\) are non-negative integers, then its decimal representation is terminating.
Options:
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
Solution
\[ \frac{3}{8} = 0.375 \] which is a terminating decimal.
Also, \(8 = 2^3\), which is of the form \(2^m \times 5^n\) (here \(n = 0\)).
So, Statement-2 correctly explains why \( \frac{3}{8} \) has a terminating decimal expansion.
- Statement-1 is true
- Statement-2 is true
- Statement-2 is the correct explanation
Final Answer
✔ Correct option: (a)