Question

Without actually performing the long division method, state whether the $\frac{13}{3125}$ will have a terminating decimals expansion or a non terminating repeating decial expansion.

Answer 1

Question:

Without actually performing the long division method, state whether the $\frac{13}{3125}$ will have a terminating decimals expansion or a non terminating repeating decial expansion.

Solution:

$\frac{13}{3125}$

$\implies \frac{13}{{5}^{5}}$

$\implies \frac{13}{{2}^{0} \times{5}^{5}}$

It's denominator is form of ${2}^{n} \times{5}^{m}.$

So, it is terminating.