Question

Which of the following fractions have terminating decimal expansion?
$\frac{1}{16},\frac{4}{25},\frac{22}{625},\frac{1}{1080}$.

Answer 1

Write fractions into their decimal form

$\frac{1}{16}=0.0625$

$\frac{4}{25}=0.26$

$\frac{22}{625}=0.0352$

$\frac{1}{1080}=\mathrm{0.000925925...}$

$\Rightarrow$In this case, the digits $925$ are recurring. So, the fraction $\frac{1}{1080}$ doesn't have terminating decimal expansion, whereas the first three terms have terminating decimal expansion as they don't have any recurring terms in their decimal expansion.