Question

Convert the following decimals as fractions:

(i) 2.3675
(ii) 54.26
(iii) 75.35
(iv) 0.7575

Answer 1

(i)
$$\begin{gathered} 2.3675=2+0.3675 \\ =2+\frac{3675}{10000} \\ =2+\frac{3675÷25}{10000÷25} \\ =2+\frac{147}{400} \\ =2\frac{147}{400} \\ =\frac{947}{400} \end{gathered}$$

(ii)
​ $$\begin{gathered} 54.26=54+0.26 \\ =54+\frac{26}{100} \\ =54+\frac{26÷2}{100÷2} \\ =54+\frac{13}{50} \\ =54\frac{13}{50} \\ =\frac{2713}{50} \end{gathered}$$

(iii)
​ $$\begin{gathered} 75.35=75+0.35 \\ =75+\frac{35}{100} \\ =75+\frac{35÷5}{100÷5} \\ =75+\frac{7}{20} \\ =75\frac{7}{20} \\ =\frac{1507}{20} \end{gathered}$$

(iv)
​ $$\begin{gathered} 0.7575=\frac{7575}{10000} \\ =\frac{7575÷25}{10000÷25} \\ =\frac{303}{400} \end{gathered}$$