Assertion (A): 1/400 has terminating decimal representation. Reason (R): ∵ 400 = 2^4 x 5^2 ∴ 1/400 has terminating decimal. 1. A is true, R is false. 2. A is false, R is true. 3. Both A and R are true. 4. Both A and R are false.

Mathematics

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Both A and R are true.

Explanation

A terminating decimal is a decimal that has a finite number of digits after the decimal point.

A fraction $\dfrac{p}{q}$ has a terminating decimal if the denominator q has only the factors 2 and 5.

In this problem, the fraction is $\dfrac{1}{400}$ . The denominator 400 can be written as: 400 = $2^4 \times 5^2$

Since the denominator has only the factors 2 and 5, the decimal representation of $\dfrac{1}{400}$ is terminating.

Hence, both Assertion (A) and Reason (R) are true.

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