Question

Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.
$-\frac{5}{10}$

Answer 1

Given that $-\frac{5}{10}=-\frac{1}{2}$

Formula: $\frac{p}{q}$ is terminating if

(i) $p$ and $q$ are co-prime and

(ii) $q$ is of the form $2^n.5^m$

where $n$ and $m$ are non-negative integers

Here $1$ and $2$ have no common factors

so, $1$ and $2$ are co-prime

for denominator $=2$

$=2^1\times 5^0$

where $n=1,m=0$

$\therefore$ $-\frac{5}{10}=-\frac{1}{2}$ is a terminating decimal