Without doing any actual division, find which of the following rational numbers have terminating decimal representation :

(i) $\dfrac{7}{16}$

(ii) $\dfrac{23}{125}$

(iii) $\dfrac{9}{14}$

(iv) $\dfrac{32}{45}$

(v) $\dfrac{43}{50}$

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

(i) $\dfrac{7}{16} = \dfrac{7}{2^4}$

So, 16 can be expressed as 2⁴ × 5⁰.

Hence, it is a terminating decimal number.

(ii) $\dfrac{23}{125} = \dfrac{23}{5^3}$

So, 125 can be expressed as 2⁰ × 5³.

Hence, it is a terminating decimal number.

(iii) $\dfrac{9}{14} = \dfrac{9}{2 \times 7}$

So, 14 cannot be expressed in form of 2^m × 5ⁿ.

Hence, it is not a terminating decimal number.

(iv) $\dfrac{32}{45} = \dfrac{32}{3^2 \times 5}$

So, 45 cannot be expressed in form of 2^m × 5ⁿ.

Hence, it is not a terminating decimal number.

(v) $\dfrac{43}{50} = \dfrac{43}{2 \times 5^2}$

So, 50 can be expressed in form of 2¹ × 5².

Hence, it is a terminating decimal number.