Convert each of the following decimals into vulgar fraction in its lowest terms :

(i) 0.65

(ii) 1.08

(iii) 0.075

(iv) 2.016

(v) 1.732

(i) Given,

$\Rightarrow 0.65 = \dfrac{65}{100}$

The H.CF. of 65 and 100 is 5, dividing the numerator and denominator by 5,

$\Rightarrow \dfrac{65 ÷ 5}{100 ÷ 5} \\[1em] \Rightarrow \dfrac{13}{20}.$

Hence, 0.65 = $\dfrac{13}{20}$.

(ii) Given,

$\Rightarrow 1.08 = \dfrac{108}{100}$

The H.CF. of 108 and 100 is 4, dividing the numerator and denominator by 4,

$\Rightarrow \dfrac{108 ÷ 4}{100 ÷ 4} \\[1em] \Rightarrow \dfrac{27}{25}$

Hence, 1.08 = $\dfrac{27}{25}$.

(iii) Given,

$\Rightarrow 0.075 = \dfrac{75}{1000}$

The H.CF. of 75 and 1000 is 25, dividing the numerator and denominator by 25,

$\Rightarrow \dfrac{75 ÷ 25}{1000 ÷ 25} \\[1em] \Rightarrow \dfrac{3}{40}$

Hence, 0.075 = $\dfrac{3}{40}$.

(iv) Given,

$\Rightarrow 2.016 = \dfrac{2016}{1000}$

The H.CF. of 2016 and 1000 is 8, dividing the numerator and denominator by 8,

$\Rightarrow \dfrac{2016 ÷ 8}{1000 ÷ 8} \\[1em] \Rightarrow \dfrac{252}{125}$

Hence, 2.016 = $\dfrac{252}{125}$.

(v) Given,

$\Rightarrow 1.732 = \dfrac{1732}{1000}$

The H.CF. of 1732 and 1000 is 4, dividing the numerator and denominator by 4

$\Rightarrow \dfrac{1732 ÷ 4}{1000 ÷ 4} \\[1em] \Rightarrow \dfrac{433}{250}$

Hence, 1.732 = $\dfrac{433}{250}$.