Percentages
Recognise the percentage as a special kind of fraction.
Percent:
A ratio whose denominator is 100. The symbol for percent is %. The model on right has 25 out of 100 squares shaded. You can say that 25 percent of the squares are shaded.
Numbers:
You can write 25 percent as \(25 \over 100\) or as 25%.
Now percentage has been deduced from percentum which mean rate per hundred or out of 100. You can see that percentage is a special kind of fraction whose denominator is 100.
1.\(11 \over 100\)means 11% 2. \(23\over 100\) means 23% 3. \(17\over 100\) means 17% 4.\(123 \over 100\) means 123%
Convert percentages to fractions, decimals and viceversa
(a)Conversion of percentage to fraction and decimal
Example 1 Convert 13% to fraction and decimal.
Solution 13% [13 out of 100]
\(13 \over 100\)= 0.13
Example 2 Convert 27% to fraction and decimal.
Solution 27% [27 out of 100]
\(27 \over 100\)= 0.27
Example Convert 137% to fraction and decimal.
Solution 137% [137 out of 100]
\(137 \over 100\)= 1.37
(b) Conversion of fraction and decimal to percentage
Example 1
Convert \(4 \over5\) to percentage
Solution:\( \frac{{4 \times 20}} {{5 \times 20}} = \frac{{80}} {{100}} \)=80%
Example 2
Convert \(3 \over 4\) to percentage.
Solution:\( \frac{{3 \times 25}} {{4 \times 25}} = \frac{{75}} {{100}} \)
Example 3
Convert \(3\over 10\) to percentage.
\( \frac{{3 \times 10}} {{10 \times 10}} = \frac{{30}} {{100}} \)
Example 4
Convert 0.19 to percentage.
Solution 0.19
\( \frac{{19}} {{100}} = 19\% \)
Example 5
Convert 0.294 to percentage.
Solution
\( \begin{gathered} = \frac{{294}} {{1000}} \hfill \\ = \frac{{294}} {{100 \times 10}} \hfill \\ = \frac{{29.4}} {{100}} = 29.4\% \hfill \\ \end{gathered} \)
Finding the percentage of a number
To find the percentage of a number, convert the given percentage into a fraction and then multiply it by the given number
Example : Find the value of 30% of 600.
Solution : 30% of 600 =\(\frac{30}{100}\times 600=\frac{18000}{100}=180\)
Expressing a quantity as a percentage of another quantity
First express the number in the form of a fraction and then convert it into a percentage.
Example : What percent of 50 is 30?
Solution :\(\frac{30}{50}\times 100%=\)\(=\frac{3000}{50}%\)=60%