Question

Without actually performing the long deviation, state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion:
$\frac{13}{3125}$

Answer 1

Let us consider factor of denominator $3125=5\times 5\times 5\times 5\times 5=5^5$

Denominator

$=5^5=2^0\times 5^5=2^0\times 5^5$

in the form $2^n{5}^m$

Where $m=0,n=5$

Thus they are terminating decimal .