Question

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.
$\frac{17}{8}$

Answer 1

We have,

$\frac{17}{8}=\frac{17}{2^3\times 5^0}$

So, the denominator 8 of the given rational number is of the form $2^m\times 5^n$, where m,n are non-negative integers.

Hence $\frac{17}{8}$ has terminating decimal expansion. the decimal expansion of $\frac{17}{8}$ terminates after $\text{max}(3,0)=3$ places of decimals.