Question

Assertion :$\frac{13}{3125}$ is a terminating decimal fraction. Reason: If $q=2^n\cdot 5^m$ where $n,m$ are non-negative integers, then $\frac{p}{q}$ is a terminating decimal fraction.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
• B. Both Assertion and Reason are correct, but Reason is not the correct explanation for Assertion.
• C. Assertion is correct, but Reason is incorrect.
• D. Assertion is incorrect, but Reason is correct.

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.

In a fraction, if the denominator is of the form $2^n\times 5^m$ then the fraction is always terminating.
In case of 3125, it can be written as,

$3125=2^0\times 5^5$

So it is terminating and reason is the correct explanation to assertion.

$\therefore$ Option A is correct.