Question

Which of the following has terminating decimal expansion?

(a) $\frac{32}{91}$
(b) $\frac{19}{80}$
(c) $\frac{23}{45}$
(d) $\frac{25}{42}$

Answer 1

(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 $(2^4\times 5)=(2^m\times 5^n)$
Hence, $\frac{19}{80}$ is a terminating decimal.