Question

Express the following fractions as decimals:

(i) $\frac{23}{10}$
(ii) $\frac{139}{100}$
(iii) $\frac{4375}{1000}$
(iv) $12\frac{1}{2}$
(v) $75\frac{1}{4}$
(vi) $25\frac{1}{8}$
(vii) $18\frac{3}{24}$
(viii) $39\frac{7}{35}$
(ix) $15\frac{1}{25}$
(x) $\frac{111}{250}$

Answer 1

(i) $\frac{23}{10}=\frac{20+3}{10}=\frac{20}{10}+\frac{3}{10}=2+\frac{3}{10}$ = 2.3

(ii) $\frac{139}{100}=\frac{100+30+9}{100}=\frac{100}{100}+\frac{30}{100}+\frac{9}{100}=1+\frac{3}{10}+\frac{9}{100}$ = 1.39

(iii) $\frac{4375}{1000}=\frac{4000+300+70+5}{1000}=\frac{4000}{1000}+\frac{300}{1000}+\frac{70}{1000}+\frac{5}{1000}=4+\frac{3}{10}+\frac{7}{100}+\frac{5}{1000}$ = 4.375

(iv) $12\frac{1}{2}=12+\frac{1}{2}$= $12+\frac{1\times 5}{2\times 5}$ = $12+\frac{5}{10}$ = 12.5

(v) $75\frac{1}{4}=75+\frac{1}{4}$$=75+\frac{1\times 25}{4\times 25}=75+\frac{25}{100}=75.25$

(vi) $25\frac{1}{8}=25+\frac{1}{8}$ = $25+\frac{1\times 125}{8\times 125}=25+\frac{125}{1000}=25.125$

(vii) $18\frac{3}{24}=18+\frac{3}{24}=18+\frac{1}{8}=18+\frac{125\times 1}{125\times 8}=18+\frac{125}{1000}=18.125$

(viii) $39\frac{7}{35}=39+\frac{7}{35}=39+\frac{1}{5}=39+\frac{1\times 2}{5\times 2}=39+\frac{2}{10}=39.2$

(ix) $15\frac{1}{25}=15+\frac{1}{25}=15+\frac{1\times 4}{25\times 4}=15+\frac{4}{100}=15.04$

(x) $\frac{111}{250}=\frac{111\times 4}{250\times 4}=\frac{444}{1000}=0.444$