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.
$\frac{15}{1600}$

Answer 1

we have,

$\frac{15}{1600}=\frac{3}{320}=\frac{3}{2^6\times 5^2}$

this means that the prime factrorization of the denominator of $\frac{15}{1600}$ s of the form $2^m\times 5^n$.

hence, it has terminating decimal expansion which terminates after $max(6,2)=6$ places of decimals.