Exercise 8A
Question 1
Express each of the following as a percentage.
(a)
(i) $\frac{1}{5}$
Sol : $\frac{1}{5} \times 100$=20%
(ii) $\frac{3}{4}$
Sol : $\frac{3}{4} \times 100$=75%
(iii) $\frac{17}{50}$
Sol : $\frac{17}{50} \times 100$=34%
(iv) $\frac{11}{20}$
Sol : $\frac{11}{20} \times 100$=55%
(v) $2\frac{9}{10}$
Sol : $\frac{29}{10}\times 100$=290%
(vi) $2\frac{8}{25}$
Sol : $\frac{58}{25}\times 100$=232%
(b)
(i) 0.3
Sol : 0.3×100=30%
(ii) 0.47
Sol : 0.89×100=89%
(iii) 0.89
Sol : 0.89×100=89%
(iv) 1.05
Sol : 1.05×100=105%
(v) 0.09
Sol : 0.09×100=9%
(vi) 0.769
Sol : 0.769×100=76.9%
(vii) 3
Sol : 3×100=300%
(viii) 9.002
Sol : 9.002×100=900.2%
(ix) 2.25
Sol : 2.25×100%
(x) 0.75
Sol : 0.75×100=75%
Question 2
Express as a fraction in its simplest form.
(a) 80%
Sol : $=\frac{80}{100}=\frac{4}{5}$
(b) 36%
Sol : $\frac{36}{100}=\frac{9}{25}$
(c) 60%
Sol : $\frac{60}{100}=\frac{3}{5}$
(d) 19%
Sol : $\frac{19}{100}$
(e) $62\frac{1}{2}$%
Sol : $\dfrac{\frac{125}{2}}{100}=\frac{125}{100}=\frac{5}{8}$
(f) $133\frac{1}{3}$%
Sol : $\dfrac{\frac{400}{3}}{100}=\frac{400}{300}=1\frac{1}{3}$
(g) 120%
Sol : $\frac{120}{100}=1\frac{1}{5}$
(h) 65%
Sol : $\frac{65}{100}=\frac{13}{20}$
(i) 270%
Sol : $\frac{270}{100}=2\frac{7}{10}$
(j) 350%
Sol : $\frac{350}{100}=\frac{7}{2}=3\frac{1}{2}$
Question 3
Express as a decimal.
(a) 7%
Sol : $\frac{7}{100}$=0.07
(b) 80%
Sol : $\frac{80}{100}$=0.8
(c) 72%
Sol : $\frac{72}{100}$ =0.72
(d) 39%
Sol : $\frac{39}{100}$=0.39
(e) $1\frac{1}{2}$%
Sol : $\frac{3}{2}=\frac{15}{100}$
=0.01
(f) $6\frac{1}{4}$%
Sol : $\frac{24}{4}=\frac{6.25}{100}$
=0.0625
(g) $27\frac{1}{2}$%
Sol : $\frac{55}{2}=\frac{27.5}{100}$
=0.275
(h) $72\frac{3}{5}$%
Sol : $\frac{363}{5}=\frac{72.6}{100}$
=0.726
(i) 189%
Sol : $\frac{189}{100}$
=1.89
(j) $205\frac{2}{5}$%
Sol : $\frac{1027}{5}=\frac{205.4}{100}$
=2.054
Question 4
Compare and Write <,> or = in the box.
(a) $\frac{5}{8}$ ___ 70%
Sol :
$\frac{5}{8}\times 100$=62.5%
$\frac{5}{8} < 70\%$
(b) 64% ___ $\frac{3}{5}$
Sol :
$\frac{3}{5}\times 100$=60%
64% >$\frac{3}{5}$
(c) 92.7% ___ 0.927
Sol :
0.927=0.927×100%=92.7%
∴92.7% = 0.927
(d) 0.99 ____ 100%
Sol :
0.99=0.99×100%=99%
∴0.99<100%
Question 5
Arrange in ascending order.
(a) 38%, 0.4, $35\frac{1}{3}$%, $\frac{5}{8}$
Sol :
0.4=0.4×100%=40%
$35\frac{1}{3}=\frac{106}{3}$=35.33%
$\frac{5}{8}=\frac{5}{8}\times 100$%=62.5%
Ans : $35\frac{1}{3}$% , 38%, 0.4, $\frac{5}{8}$
(b) 0.93, 19.20, $1\frac{2}{3}$, 67%
Sol :
Question 6
Arrange in descending order.
(a) $\frac{4}{5}$, 0.5, 500%,$66\frac{2}{3}$%
Sol :
(b) $\frac{7}{20}$, 0.038, 39%, 0.59
Sol :
Question 7
Use the following diagrams to complete the table
(a)
| Fraction shaded | Percentage shaded | Percentage unshaded | |
|---|---|---|---|
| (a) | $\frac{3}{4}$ | 75% | 25% |
| (b) | $\frac{9}{15}=\frac{3}{5}$ | 60% | 40% |
| (c) | $\frac{2}{5}$ | 40% | 60% |
| (d) | $\frac{5}{8}$ | $62\frac{1}{2}$% | $37\frac{1}{2}$% |
Question 8
A molecular of water is made up of 2 atoms of hydrogen and 1 atom of oxygen. What percent of the atoms a water molecular is oxygen?
Sol :
∴Percentage of oxygen in water $=\frac{1}{3}\times 100$%$=33\frac{1}{3}$%
Question 9
Sterling silver is an alloy combining 925 parts of pure silver and 75 parts of another metal, such as copper. What percent of sterling silver is not pure silver?
Sol :
∴Percentage of sterling silver$=\frac{75}{(925+75)}\times 100$%
$=\frac{75}{1000}\times 100$
=7.5%
Question 10
Prashant spends 4 hours a day on his self study, 1 hour playing video games and 1 hour in doing workouts at fitness centre. What per cent of the day does Prahant spend on these activities?
Sol :
∴Prashant spend time on these activities
$=\frac{(4+1+1)}{24}\times 100$%
$=\frac{6}{24}\times 100$%
=25%
