Question

Without actually performing the long division state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion .

$\frac{15}{1600}$.

Answer 1

If the denominator has factors in the form of $2^m\times 5^n$ then it has a terminating decimal expansion.

If the denominator has factors other than $2$ and $5$ then it has a non-terminating decimal expansion.

Factorizing the denominator, we get,

$1600=2^6\times 5^2$

As the denominator is in the form of $2^m\times 5^n$ .

Hence, $\frac{15}{1600}$ has a terminating decimal expansion.