Percent — Exercise 10(A)

Express the following statement in percentage form:

13 out of 20

Answer

To express a statement in the percentage form, write it as a fraction and then multiply the fraction by 100 and write the percentage sign.

⇒ 13 out of 20

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

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

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

⇒ 65%

Hence, 13 out of 20 = 65%.

Express the following statement in percentage form:

21 eggs out of 30 are good

Answer

To express a statement in the percentage form, write it as a fraction and then multiply the fraction by 100 and write the percentage sign.

⇒ 21 eggs out of 30 are good

$\Rightarrow \dfrac{21}{30}$ eggs are good

$\Rightarrow \left(\dfrac{21}{30} \times 100\right)$% eggs are good

$\Rightarrow \dfrac{2100}{30}$% eggs are good

⇒ 70% eggs are good

Hence, 70% of the eggs are good.

Express the following fraction as percent:

$\dfrac{3}{200}$

Answer

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

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

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

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

⇒ 1.5%

Hence, $\mathbf{\dfrac{3}{200} = 1.5}$%.

Express the following fraction as percent:

$\dfrac{5}{6}$

Answer

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\dfrac{5}{6} \times 100\right)$%

$\Rightarrow \dfrac{500}{6}$%

$\Rightarrow \dfrac{250}{3}$%

$\Rightarrow 83\dfrac{1}{3}$%

Hence, $\mathbf{\dfrac{5}{6} = 83\dfrac{1}{3}}$%.

Express the following fraction as percent:

$\dfrac{65}{80}$

Answer

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\dfrac{65}{80} \times 100\right)$%

$\Rightarrow \dfrac{6500}{80}$%

$\Rightarrow \dfrac{325}{4}$%

$\Rightarrow 81\dfrac{1}{4}$% = 81.25%

Hence, $\mathbf{\dfrac{65}{80} = 81\dfrac{1}{4}}$% = 81.25%.

Express the following fraction as percent:

$\dfrac{2}{3}$

Answer

To convert a given fraction into percentage (percent form), multiply the given fraction by 100 and write the percentage sign.

$\Rightarrow \left(\dfrac{2}{3} \times 100\right)$%

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

$\Rightarrow 66\dfrac{2}{3}$%

Hence, $\mathbf{\dfrac{2}{3} = 66\dfrac{2}{3}}$%.

Express as percent:

0.10

Answer

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.10 × 100)%

⇒ 10%

Hence, 0.10 = 10%.

Express as percent:

0.02

Answer

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.02 × 100)%

⇒ 2%

Hence, 0.02 = 2%.

Express as percent:

0.7

Answer

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.7 × 100)%

⇒ 70%

Hence, 0.7 = 70%.

Express as percent:

0.15

Answer

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.15 × 100)%

⇒ 15%

Hence, 0.15 = 15%.

Express as percent:

0.032

Answer

To convert a given decimal into percentage (percent form), multiply the given decimal by 100 and write the percentage sign.

⇒ (0.032 × 100)%

⇒ 3.2%

Hence, 0.032 = 3.2%.

Convert the following into a fraction in its lowest terms:

8%

Answer

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \dfrac{8}{100}$

$\Rightarrow \dfrac{2}{25}$

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

Convert the following into a fraction in its lowest terms:

20%

Answer

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \dfrac{20}{100}$

$\Rightarrow \dfrac{1}{5}$

Hence, 20% = $\mathbf{\dfrac{1}{5}}$.

Convert the following into a fraction in its lowest terms:

85%

Answer

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \dfrac{85}{100}$

$\Rightarrow \dfrac{17}{20}$

Hence, 85% = $\mathbf{\dfrac{17}{20}}$.

Convert the following into a fraction in its lowest terms:

250%

Answer

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

$\Rightarrow \dfrac{250}{100} \\[1em] \Rightarrow \dfrac{5}{2} \\[1em] \Rightarrow 2\dfrac{1}{2}$

Hence, 250% = $\mathbf{\dfrac{5}{2} = 2\dfrac{1}{2}}$.

Convert the following into a fraction in its lowest terms:

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

Answer

To convert a given percentage into a fraction, remove the sign of percentage and divide by 100. Then reduce the resulting fraction to its lowest terms.

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

$\Rightarrow \dfrac{25}{2} \times \dfrac{1}{100}$

$\Rightarrow \dfrac{25}{200}$

$\Rightarrow \dfrac{1}{8}$

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

Express as a decimal fraction:

25%

Answer

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \dfrac{25}{100}$

⇒ 0.25

Hence, 25% = 0.25.

Express as a decimal fraction:

108%

Answer

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \dfrac{108}{100}$

⇒ 1.08

Hence, 108% = 1.08.

Express as a decimal fraction:

95%

Answer

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \dfrac{95}{100}$

⇒ 0.95

Hence, 95% = 0.95.

Express as a decimal fraction:

4.5%

Answer

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \dfrac{4.5}{100}$

⇒ 0.045

Hence, 4.5% = 0.045.

Express as a decimal fraction:

29.2%

Answer

To convert a given percentage into a decimal, remove the sign of percentage and divide by 100.

$\Rightarrow \dfrac{29.2}{100}$

⇒ 0.292

Hence, 29.2% = 0.292.

Express the following number as percent:

7

Answer

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (7 × 100)%

⇒ 700%

Hence, 7 expressed as a percent is 700%.

Express the following number as percent:

2

Answer

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (2 × 100)%

⇒ 200%

Hence, 2 expressed as a percent is 200%.

Express the following number as percent:

19.5

Answer

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (19.5 × 100)%

⇒ 1950%

Hence, 19.5 expressed as a percent is 1950%.

Express the following number as percent:

5.37

Answer

To express a given number as percent, multiply the number by 100 and write the sign of percentage.

⇒ (5.37 × 100)%

⇒ 537%

Hence, 5.37 expressed as a percent is 537%.