Without actual division, find which of the following fractions are terminating decimals :

(i) $\dfrac{9}{25}$

(ii) $\dfrac{7}{12}$

(iii) $\dfrac{13}{16}$

(iv) $\dfrac{25}{128}$

(v) $\dfrac{9}{50}$

(vi) $\dfrac{121}{125}$

(vii) $\dfrac{19}{55}$

(viii) $\dfrac{37}{78}$

(ix) $\dfrac{23}{80}$

(x) $\dfrac{19}{30}$

In rational numbers, if the denominator of the fraction can be expressed in the form of 2^m. × 5^n., then it is a terminating decimal.

(i) So, 25 can be expressed as 2^0. × 5^2., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{9}{25}$ is a terminating decimal number.

(ii) So, 12 can be expressed as 3 × 2^2. × 5^0., which is not in the form of 2^m. × 5^n..

Hence, $\dfrac{7}{12}$ is not a terminating decimal number.

(iii) So, 16 can be expressed as 2^4. × 5^0., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{13}{16}$ is a terminating decimal number.

(iv) So, 128 can be expressed as 2^7. × 5^0., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{25}{128}$ is a terminating decimal number.

(v) So, 50 can be expressed as 2^1. × 5^2., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{9}{50}$ is a terminating decimal number.

(vi) So, 125 can be expressed as 2^0. × 5^3., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{121}{125}$ is a terminating decimal number.

(vii) So, 55 can be expressed as 11 × 2^0. × 5^1., which is not in the form of 2^m. × 5^n..

Hence, $\dfrac{19}{55}$ is not a terminating decimal number.

(viii) So, 78 can be expressed as 39 × 2^1. × 5^0., which is not in the form of 2^m. × 5^n..

Hence, it is not a terminating decimal number.

(ix) So, 80 can be expressed as 2^4. × 5^1., which is in the form of 2^m. × 5^n..

Hence, $\dfrac{23}{80}$ is a terminating decimal number.

(x) So, 30 can be expressed as 3 × 2^1. × 5^1., which is not in the form of 2^m. × 5^n..

Hence, $\dfrac{19}{30}$ is not a terminating decimal number.