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

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Solution

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 $n = 1, m = 0$
$∴$ $- \frac{5}{10} = - \frac{1}{2}$ is a terminating decimal

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