Which of the following has terminating decimal expansion?
Question:

Which of the following has terminating decimal expansion?

(a) $\frac{32}{91}$

(b) $\frac{19}{80}$

(c) $\frac{23}{45}$

(d) $\frac{25}{42}$

Solution:

(b) $\frac{19}{80}$

$\frac{19}{80}=\frac{19}{2^{4} \times 5}$

We know 2 and 5 are not factors of 19, so it is in its simplest form.

And $\left(2^{4} \times 5\right)=\left(2^{m} \times 5^{n}\right)$

Hence, $\frac{19}{80}$ is a terminating decimal.