Without actual division, find which of the following rationals are terminating decimals.

(i) (ii) (iii)

(iv) (v)

First we have to know what is terminating decimal. Terminating decimal is the number which has digits that do not go on forever.

(i)

Denominator 80 has factors = 2 × 2 × 2 × 2 × 5

So, 80 has no prime factors other than 2 and 5, thus is terminating decimal.

(ii)

Denominator 24 has factors = 2 × 2 × 2 × 3

So, 24 has factors other than 2 and 5, thus is not a terminating decimal.

(iii)

Denominator 12 has factors = 2 × 2 × 3

So, 12 has factors other than 2 and 5, thus is not a terminating decimal.

(iv)

Denominator 35 has factors = 5 × 7

So, 35 has factors other than 2 and 5, thus is not a terminating decimal.

(v)

Denominator 24 has factors = 5 × 5 × 5

So, 125 has no prime factors other than 2 and 5, thus is a terminating decimal.