Without actual division, show that each of the rational numbers given below is expressible as a terminating decimal :

(i) $\dfrac{11}{16}$

(ii) $\dfrac{17}{20}$

(iii) $\dfrac{44}{125}$

(iv) $\dfrac{9}{80}$

(v) $\dfrac{123}{200}$

(vi) $\dfrac{129}{320}$

(vii) $\dfrac{431}{500}$

(viii) $\dfrac{807}{1250}$

(i) $\dfrac{11}{16}$

The given number is $\dfrac{11}{16}$.

Its denominator is $16 = 2^4$.

Thus, the denominator of $\dfrac{11}{16}$ has no prime factor other than 2.

∴ $\dfrac{11}{16}$ is expressible as a terminating decimal.

(ii) $\dfrac{17}{20}$

The given number is $\dfrac{17}{20}$.

Its denominator is $20 = 2^2 \times 5^1$.

Thus, the denominator of $\dfrac{17}{20}$ has no prime factor other than 2 and 5.

∴ $\dfrac{17}{20}$ is expressible as a terminating decimal.

(iii) $\dfrac{44}{125}$

The given number is $\dfrac{44}{125}$.

Its denominator is $125 = 5^3$.

Thus, the denominator of $\dfrac{44}{125}$ has no prime factor other than 5.

∴ $\dfrac{44}{125}$ is expressible as a terminating decimal.

(iv) $\dfrac{9}{80}$

The given number is $\dfrac{9}{80}$.

Its denominator is $80 = 2^4 \times 5^1$.

Thus, the denominator of $\dfrac{9}{80}$ has no prime factor other than 2 and 5.

∴ $\dfrac{9}{80}$ is expressible as a terminating decimal.

(v) $\dfrac{123}{200}$

The given number is $\dfrac{123}{200}$.

Its denominator is $200 = 2^3 \times 5^2$.

Thus, the denominator of $\dfrac{123}{200}$ has no prime factor other than 2 and 5.

∴ $\dfrac{123}{200}$ is expressible as a terminating decimal.

(vi) $\dfrac{129}{320}$

The given number is $\dfrac{129}{320}$.

Its denominator is $320 = 2^6 \times 5^1$.

Thus, the denominator of $\dfrac{129}{320}$ has no prime factor other than 2 and 5.

∴ $\dfrac{129}{320}$ is expressible as a terminating decimal.

(vii) $\dfrac{431}{500}$

The given number is $\dfrac{431}{500}$.

Its denominator is $500 = 2^2 \times 5^3$.

Thus, the denominator of $\dfrac{431}{500}$ has no prime factor other than 2 and 5.

∴ $\dfrac{431}{500}$ is expressible as a terminating decimal.

(viii) $\dfrac{807}{1250}$

The given number is $\dfrac{807}{1250}$.

Its denominator is $1250 = 2^1 \times 5^4$.

Thus, the denominator of $\dfrac{807}{1250}$ has no prime factor other than 2 and 5.

∴ $\dfrac{807}{1250}$ is expressible as a terminating decimal.