Question

Question 1 (iv)
Without actually performing the long division, state whether $\frac{15}{1600}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Answer 1

$\frac{15}{1600}$
Factorising the denominator, we get;
$1600=2\times 2\times 2\times 2\times 2\times 2\times 5\times 5=2^6\times 5^2$
Here, the denominator is in the form of $2^m\times 5^n$, where m = 6 and n = 2.
Thus, the rational number $\frac{15}{1600}$ has a terminating decimal expansion.