Without finding the decimal representation, state whether the following rational numbers are terminating decimal or non-terminating decimals.

Foundation

Mathematics Foundation

Properties of Real Number

Recurring Decimal Number

Linear Equations in One Variable

Question

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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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 2n.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