Percentage — Exercise 10(A)

Express the following as a fraction in its lowest terms:

8%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 8%

$\Rightarrow 8 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{8}{100}\\[1em] \Rightarrow \dfrac{2}{25}$

Hence, 8% = $\mathbf{\dfrac{2}{25}}$.

Express the following as a fraction in its lowest terms:

36%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 36%

$\Rightarrow 36 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{36}{100}\\[1em] \Rightarrow \dfrac{9}{25}$

Hence, 36% = $\mathbf{\dfrac{9}{25}}$.

Express the following as a fraction in its lowest terms:

125%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 125%

$\Rightarrow 125 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{125}{100}\\[1em] \Rightarrow \dfrac{5}{4}$

Hence, 125% = $\mathbf{\dfrac{5}{4}}$.

Express the following as a fraction in its lowest terms:

$12\dfrac{1}{2}$%

Answer

⇒ $12\dfrac{1}{2}$% = $\dfrac{25}{2}$%

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

$\Rightarrow \dfrac{25}{2} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{25}{200}\\[1em] \Rightarrow \dfrac{1}{8}$

Hence, $\mathbf{12\dfrac{1}{2}}$% = $\mathbf{\dfrac{1}{8}}$.

Express the following as a fraction in its lowest terms:

$26\dfrac{2}{3}$%

Answer

⇒ $26\dfrac{2}{3}$% = $\dfrac{80}{3}$%

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

$\Rightarrow \dfrac{80}{3} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{80}{300}\\[1em] \Rightarrow \dfrac{4}{15}$

Hence, $\mathbf{26\dfrac{2}{3}}$% = $\mathbf{\dfrac{4}{15}}$.

Express the following as a fraction in its lowest terms:

9.6%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 9.6%

$\Rightarrow 9.6 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{9.6}{100}\\[1em] \Rightarrow \dfrac{96}{1000}\\[1em] \Rightarrow \dfrac{12}{125}$

Hence, 9.6% = $\mathbf{\dfrac{12}{125}}$.

Express the following as a fraction in its lowest terms:

0.36%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ 0.36%

$\Rightarrow 0.36 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{0.36}{100}\\[1em] \Rightarrow \dfrac{36}{10000}\\[1em] \Rightarrow \dfrac{9}{2500}$

Hence, 0.36% = $\mathbf{\dfrac{9}{2500}}$.

Express the following as a fraction in its lowest terms:

$\dfrac{4}{5}$%

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$ and reduce the fraction to its lowest terms.

⇒ $\dfrac{4}{5}$%

$\Rightarrow \dfrac{4}{5} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{4}{500}\\[1em] \Rightarrow \dfrac{1}{125}$

Hence, $\mathbf{\dfrac{4}{5}}$% = $\mathbf{\dfrac{1}{125}}$.

Express each of the following as a decimal:

43%

Answer

To convert a percentage into a decimal, replace the % sign with $\dfrac{1}{100}$ and express the fraction as a decimal.

⇒ 43%

$\Rightarrow 43 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{43}{100}\\[1em] \Rightarrow 0.43$

Hence, 43% = 0.43.

Express each of the following as a decimal:

7%

Answer

To convert a percentage into a decimal, replace the % sign with $\dfrac{1}{100}$ and express the fraction as a decimal.

⇒ 7%

$\Rightarrow 7 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{7}{100}\\[1em] \Rightarrow 0.07$

Hence, 7% = 0.07.

Express each of the following as a decimal:

120%

Answer

To convert a percentage into a decimal, replace the % sign with $\dfrac{1}{100}$ and express the fraction as a decimal.

⇒ 120%

$\Rightarrow 120 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{120}{100}\\[1em] \Rightarrow 1.2$

Hence, 120% = 1.2.

Express each of the following as a decimal:

3.5%

Answer

To convert a percentage into a decimal, replace the % sign with $\dfrac{1}{100}$ and express the fraction as a decimal.

⇒ 3.5%

$\Rightarrow 3.5 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{3.5}{100}\\[1em] \Rightarrow 0.035$

Hence, 3.5% = 0.035.

Express each of the following as a ratio:

56%

Answer

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 56%

$\Rightarrow 56 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{56}{100}\\[1em] \Rightarrow \dfrac{14}{25}\\[1em] \Rightarrow 14 : 25$

Hence, 56% = 14 : 25.

Express each of the following as a ratio:

$16\dfrac{2}{3}$%

Answer

⇒ $16\dfrac{2}{3}$% = $\dfrac{50}{3}$%

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

$\Rightarrow \dfrac{50}{3} \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{50}{300}\\[1em] \Rightarrow \dfrac{1}{6}\\[1em] \Rightarrow 1 : 6$

Hence, $\mathbf{16\dfrac{2}{3}}$% = 1 : 6.

Express each of the following as a ratio:

6.4%

Answer

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 6.4%

$\Rightarrow 6.4 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{6.4}{100}\\[1em] \Rightarrow \dfrac{64}{1000}\\[1em] \Rightarrow \dfrac{8}{125}\\[1em] \Rightarrow 8 : 125$

Hence, 6.4% = 8 : 125.

Express each of the following as a ratio:

0.8%

Answer

To convert a percentage into a ratio, first convert the percentage into a fraction in its lowest terms and then write the fraction as a ratio.

⇒ 0.8%

$\Rightarrow 0.8 \times \dfrac{1}{100}\\[1em] \Rightarrow \dfrac{0.8}{100}\\[1em] \Rightarrow \dfrac{8}{1000}\\[1em] \Rightarrow \dfrac{1}{125}\\[1em] \Rightarrow 1 : 125$

Hence, 0.8% = 1 : 125.

Express 15% as a (i) fraction (ii) decimal (iii) ratio.

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$; the fraction may then be written as a decimal or a ratio, as desired.

(i) As a fraction:

⇒ 15%

$\Rightarrow \dfrac{15}{100}$

$\Rightarrow \dfrac{3}{20}$

Hence, 15% as a fraction = $\mathbf{\dfrac{3}{20}}$.

(ii) As a decimal:

⇒ 15%

$\Rightarrow \dfrac{15}{100}$

$\Rightarrow 0.15$

Hence, 15% as a decimal = 0.15

(iii) As a ratio:

⇒ 15%

$\Rightarrow \dfrac{15}{100}$

$\Rightarrow \dfrac{3}{20}$

⇒ 3 : 20

Hence, 15% as a ratio = 3 : 20.

Express 136% as a (i) fraction (ii) decimal (iii) ratio.

Answer

To convert a percentage into a fraction, replace the % sign with $\dfrac{1}{100}$; the fraction may then be written as a decimal or a ratio, as desired.

(i) As a fraction:

⇒ 136%

$\Rightarrow \dfrac{136}{100}$

$\Rightarrow \dfrac{34}{25}$

Hence, 136% as a fraction = $\mathbf{\dfrac{34}{25}}$.

(ii) As a decimal:

⇒ 136%

$\Rightarrow \dfrac{136}{100}$

$\Rightarrow \dfrac{34}{25}$

$\Rightarrow 1.36$

Hence, 136% as a decimal = 1.36

(iii) As a ratio:

⇒ 136%

$\Rightarrow \dfrac{136}{100}$

$\Rightarrow \dfrac{34}{25}$

$\Rightarrow 34 : 25$

Hence, 136% as a ratio = 34 : 25.

Convert each of the following fractions into a percentage:

$\dfrac{13}{20}$

Answer

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \dfrac{13}{20}$

$\Rightarrow \left(\dfrac{13}{20} \times 100\right)$%

$\Rightarrow \dfrac{1300}{20}$%

$\Rightarrow 65$%

Hence, $\mathbf{\dfrac{13}{20}}$ = 65%.

Convert each of the following fractions into a percentage:

$\dfrac{7}{16}$

Answer

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \dfrac{7}{16}$

$\Rightarrow \left(\dfrac{7}{16} \times 100\right)$%

$\Rightarrow \dfrac{700}{16}$%

$\Rightarrow \dfrac{175}{4}$%

$\Rightarrow 43\dfrac{3}{4}$%

Hence, $\mathbf{\dfrac{7}{16}}$ = $\mathbf{43\dfrac{3}{4}}$%.

Convert each of the following fractions into a percentage:

$\dfrac{5}{12}$

Answer

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \dfrac{5}{12}$

$\Rightarrow \left(\dfrac{5}{12} \times 100\right)$%

$\Rightarrow \dfrac{500}{12}$%

$\Rightarrow \dfrac{125}{3}$%

$\Rightarrow 41\dfrac{2}{3}$%

Hence, $\mathbf{\dfrac{5}{12}}$ = $\mathbf{41\dfrac{2}{3}}$%.

Convert each of the following fractions into a percentage:

$2\dfrac{3}{4}$

Answer

⇒ $2\dfrac{3}{4} = \dfrac{11}{4}$

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \left(\dfrac{11}{4} \times 100\right)$%

$\Rightarrow \dfrac{1100}{4}$%

$\Rightarrow 275$%

Hence, $\mathbf{2\dfrac{3}{4}}$ = 275%.

Convert each of the following fractions into a percentage:

$1\dfrac{7}{8}$

Answer

⇒ $1\dfrac{7}{8} = \dfrac{15}{8}$

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \left(\dfrac{15}{8} \times 100\right)$%

$\Rightarrow \dfrac{1500}{8}$%

$\Rightarrow \dfrac{375}{2}$%

$\Rightarrow 187\dfrac{1}{2}$%

Hence, $\mathbf{1\dfrac{7}{8}}$ = $\mathbf{187\dfrac{1}{2}}$%.

Convert each of the following fractions into a percentage:

$\dfrac{3}{200}$

Answer

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \dfrac{3}{200}$

$\Rightarrow \left(\dfrac{3}{200} \times 100\right)$%

$\Rightarrow \dfrac{300}{200}$%

$\Rightarrow \dfrac{3}{2}$%

$\Rightarrow 1\dfrac{1}{2}$%

Hence, $\mathbf{\dfrac{3}{200}}$ = $\mathbf{1\dfrac{1}{2}}$%.

Convert each of the following fractions into a percentage:

$\dfrac{24}{5}$

Answer

To convert a fraction into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow \dfrac{24}{5}$

$\Rightarrow \left(\dfrac{24}{5} \times 100\right)$%

$\Rightarrow \dfrac{2400}{5}$%

$\Rightarrow 480$%

Hence, $\mathbf{\dfrac{24}{5}}$ = 480%.

Convert each of the following fractions into a percentage:

3

Answer

To convert a number into a percentage, multiply it by 100 and put the % sign.

$\Rightarrow 3$

$\Rightarrow (3 \times 100)$%

$\Rightarrow 300$%

Hence, 3 = 300%.

Convert each of the following decimals into a percentage:

0.7

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 0.7

⇒ (0.7 × 100)%

⇒ 70%

Hence, 0.7 = 70%.

Convert each of the following decimals into a percentage:

0.54

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 0.54

⇒ (0.54 × 100)%

⇒ 54%

Hence, 0.54 = 54%.

Convert each of the following decimals into a percentage:

0.06

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 0.06

⇒ (0.06 × 100)%

⇒ 6%

Hence, 0.06 = 6%.

Convert each of the following decimals into a percentage:

0.073

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 0.073

⇒ (0.073 × 100)%

⇒ 7.3%

Hence, 0.073 = 7.3%.

Convert each of the following decimals into a percentage:

2.05

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 2.05

⇒ (2.05 × 100)%

⇒ 205%

Hence, 2.05 = 205%.

Convert each of the following decimals into a percentage:

4.3

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 4.3

⇒ (4.3 × 100)%

⇒ 430%

Hence, 4.3 = 430%.

Convert each of the following decimals into a percentage:

1.065

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 1.065

$\Rightarrow \Big(\dfrac{1065}{1000} \times 100\Big)$%

$\Rightarrow 106\dfrac{1}{2}$%

Hence, 1.065 = $\mathbf{106\dfrac{1}{2}}$%.

Convert each of the following decimals into a percentage:

0.005

Answer

To convert a decimal into a percentage, multiply it by 100 and put the % sign.

⇒ 0.005 or $\dfrac{5}{1000}$

$\Rightarrow \Big(\dfrac{5}{1000} \times 100 \Big)$%

$\Rightarrow \dfrac{1}{2}$%

Hence, 0.005 = $\mathbf{\dfrac{1}{2}}$%.