Question

Without actual division find which of the following rationals are terminating decimal:

• A. $\frac{13}{80}$
• B. $\frac{7}{28}$
• C. $\frac{5}{12}$
• D. $\frac{8}{35}$
• E. $\frac{16}{125}$

Answer 1

The correct option is A

$\frac{13}{80}$

Explanation.

For terminating decimal the prime factorization of denominator should only contain factor of the form $2^m\times 5^n$.

The prime factorization of $\frac{13}{80}=\frac{13}{2^4\times 5}$. Hence, terminating.

The prime factorization of $\frac{7}{28}=\frac{7}{2^2\times 7}$. Hence, non-terminating.

The prime factorization of $\frac{5}{12}=\frac{5}{2^2\times 3}$.Hence, non-terminating.

The prime factorization of $\frac{8}{35}=\frac{8}{7\times 5}$.Hence, non- terminating.

The prime factorization of $\frac{16}{125}=\frac{16}{5^3}$.Hence, non-terminating.

Hence, the correct option is $\mathrm{A}$.