Question

Alan rewrites a fraction less than $1$ as a decimal. A numerator is a whole number greater than $0$. For which denominator will the fraction always convert to a terminating decimal?

• A. $12$
• B. $16$
• C. $13$
• D. $9$

Answer 1

The correct option is B

$16$

Explanation for the correct answer:

For decimal to be terminating, the denominator of the fraction must be of the form $2^{\mathrm{m}}\times 5^{\mathrm{n}}$

As, $16=2^4$

Thus, for denominator $16$, the fraction will always convert to a terminating decimal.

Explanation for the incorrect answer.

For decimal to be terminating, the denominator of the fraction must be of the form $2^{\mathrm{m}}\times 5^{\mathrm{n}}$.

As, $12=2^2\times 3$

And, $13=1\times 13$

And, $9=3^2$

Thus, for denominator $12,13$ and $9$, the fraction will never convert to a terminating decimal.

Hence, the correct option is (B).