RD Sharma solution class 8 chapter 12 Percentage Exercise 12.1

Exercise 12.1

Page-12.2

Question 1:

Write each of the following as percent:
(i) $\frac{7}{25}$
(ii) $\frac{14}{625}$
(iii) $\frac{5}{8}$
(iv) 0.8
(v) 0.005
(vi) 3 : 25
(vii) 11 : 80
(viii) 111 : 125
(ix) 13 : 75
(x) 15 : 16
(xi) 0.18
(xii) $\frac{7}{125}$

Answer 1:

$$\begin{gathered} \left(\mathrm{i}\right) \frac{7}{25}=\frac{7}{25}\times 100 \\ =\frac{700}{25}=28\% \\ \left(\mathrm{ii}\right) \frac{14}{625}=\frac{14}{25\times 25}\times 100 \\ =\frac{1400}{625} \\ =2.24\% \\ \left(\mathrm{iii}\right) \frac{5}{8}=0.625\times 100 \\ =62.5\% \\ \left(\mathrm{iv}\right) 0.8=\frac{8}{10}\times 100 \\ =80\% \\ \left(\mathrm{v}\right) 0.005=0.005\times 100 \\ =0.5\% \\ \left(\mathrm{vi}\right) 3:25=\frac{3}{25}\times 100 \\ =\frac{300}{25} \\ =12\% \\ \left(\mathrm{vii}\right) 11:80=\frac{11}{80}\times 100 \\ =\frac{1100}{80} \\ =13.75\% \\ \left(\mathrm{viii}\right) 111:125=\frac{111}{125} \\ =0.888\times 100 \\ =88.8\% \\ \left(\mathrm{ix}\right) 13:75=\frac{13}{75} \\ =0.1733\times 100 \\ =17.33\% \\ \left(\mathrm{x}\right) 15:16=\frac{15}{16} \\ =0.9375\times 100 \\ =93.75\% \\ \left(\mathrm{xi}\right) 0.18=\frac{18}{100} \\ =\frac{18}{100}\times 100 \\ =18\% \\ \left(\mathrm{xii}\right) \frac{7}{125}=0.056 \\ =0.056\times 100 \\ =5.6\% \end{gathered}$$

Question 2:

Convert the following percentages to fractions and ratios:
(i) 25%
(ii) 2.5%
(iii) 0.25%
(iv) 0.3%
(v) 125%

Answer 2:

$$\begin{gathered} \left(\mathrm{i}\right) 25\%=\frac{25}{100} \\ =\frac{5}{20}=\frac{1}{4} \\ \therefore \mathrm{Ratio}=1:4 \\ \left(\mathrm{ii}\right) 2.5\%=\frac{2.5}{100} \\ =\frac{25}{1000}=\frac{5}{200} \\ =\frac{1}{40} \\ \therefore \mathrm{Ratio}=1:40 \\ \left(\mathrm{iii}\right) 0.25\%=\frac{0.25}{100} \\ =\frac{25}{10000}=\frac{5}{2000} \\ =\frac{1}{400} \\ \therefore \mathrm{Ratio}=1:400 \\ \left(\mathrm{iv}\right) 0.3\%=\frac{0.3}{100} \\ =\frac{3}{1000} \\ \therefore \mathrm{Ratio}=3:1000 \\ \left(\mathrm{v}\right) 125\%=\frac{125}{100} \\ =\frac{5}{4} \\ \therefore \mathrm{Ratio}=5:4 \end{gathered}$$

Question 3:

Express the following as decimal fractions:
(i) 27%
(ii) 6.3%
(iii) 32%
(iv) 0.25%
(v) 7.5%
(vi) $\frac{1}{8}\%$

Answer 3:

$$\begin{gathered} \left(\mathrm{i}\right) 27\%=\frac{27}{100} \\ =0.27 \\ \left(\mathrm{ii}\right) 6.3\%=\frac{6.3}{100} \\ =0.063 \\ \left(\mathrm{iii}\right) 32\%=\frac{32}{100} \\ =0.32 \\ \left(\mathrm{iv}\right) 0.25\%=\frac{0.25}{100} \\ =0.0025 \\ \left(\mathrm{v}\right) 7.5\%=\frac{7.5}{100} \\ =0.075 \\ \left(\mathrm{vi}\right) \frac{1}{8}\%=\frac{1}{8}\times \frac{1}{100} \\ =\frac{1}{800} \\ =0.00125 \end{gathered}$$