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.