Question

Question 1 (i)
Without actually performing the long division, state whether $\frac{13}{3125}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Answer 1

$\frac{13}{3125}$
On factorising the denominator, we get,
$3125=5\times 5\times 5\times 5\times 5=5^5$
Here, the denominator is in the form of $2^m\times 5^n$, where m = 0 and n = 5.
It means that the rational number $\frac{13}{3125}$ has a terminating decimal expansion.