Percentages are an important part of our everyday lives. We use percentages in different areas. Such as % discount in shopping malls, % rainfall of the year, bank interest rates, % housing loan, % of the girl passed in 10th class, % rate of petrol and diesel. Percentages are a useful way of comparing fractions with different denominators. Percentages give information which is often easier to understand than fractions.
Example: of the total number of students in the class are male, is quite difficult to interpret, while the statement 45% of the total number of students in the class are male is easier to understand
Meaning of Percentage:
Percent: The word percent is derived from the Latin word ‘percentum’ which means ‘per hundred’.
Percentage: Percentage are numerators of fractions with denominator 100. The percentage is denoted by the symbol ‘%’ i.e., 1 % means 1 out of 100. It can be written as 1%= 1/100=0.01
Example: When we say Rakesh gives 20% of his income as income tax, this means that he gives ₹ 20 out of every hundred rupees of his income.
To understand this let us consider the following example.
Aniket is fond of collecting souvenirs. He collected 100 souvenirs from different countries. From the table can you tell the percentage of souvenirs of any country?
Percentages when the total is not a hundred
In such cases, we need to convert the fractions to an equivalent fraction with denominator 100.
Any fraction can be expressed into a percentage by multiplying it by 100.
We multiply the fraction by 100/100. This does not change the value of the fraction.
Example: Write as a percent.
=×= (× 100) % = ( )%=12%
Example: Write as a percent.
= x = (× 100) % = ( )%=5%
Example: There are 50 students in class VII, and 35 go to the picnic. Calculate the percentage of the number of students who go to the picnic?
35 students of the 50 go to the picnic.
Percentage of the number of students in class VII = ×
= (× 100) % = = 70%
So, 70% of the students go to the picnic
Converting fractional numbers to Percentage
To convert a fractional number into percentages, multiply the fraction by 100 and put the % sign.
Example: Convert the fractional number into percent.
= × = ( × 100)%= ( )%= 6%
Example: Convert the fractional number into percent.
= × = ( × 100)%= ( )%=12.5%
Converting Decimals to Percentage
To convert a decimal number into a percentage, multiply the decimal number by 100 and put the % sign.
Express each of the following decimal number into percent.
(i) 0.55 (ii) 0.07 (iii) 2.2
(i) 0.55 = 0.55 × 100% = × 100% = 55 %
(ii) 0.07 = 0.07 × 100% = × 100% = 7%
(iii) 2.2 = 2.2 × 100% = × 100% = 220%
Converting Percentages to fraction or decimals
To convert a percentage into a fraction or a decimal, divide it by 100%.
Express 140 % percentage into a fraction.
140 % = = =
Express 140 % percentage into a decimal.
140 % = = 1.40
Express 3 % percentage into a decimal.
3 % = = 0. 03
Express 20 % percentage into a fraction.
20 % = =
Percentage – Concept of Whole
The percentage is also used as the concept of the whole. Suppose if we add parts together it always gives a whole (100%). Similarly, if the whole is divided into parts it combines and gives you a whole or 100%.
Example: As we know the air is a mixture of gases and that gases are present in the atmosphere in different percentages. When we add the percentage of different gases in the atmosphere we get 100%
So, if we are given one part, we can always find out the other part. Suppose Rashmi has 1 whole pizza, it consists of 8 parts out of these Rashmi gives 4 parts to her brother, we can always find out the remaining parts of the pizza.
Example: In a school, 30% students are girls, find the percentage of boys.
Total number of students in the school = 100%
Percentage of girls in a school = 30%
The percentage of boys in a school = Total number of students in the school (100%) – Percentage of girls in a school
The percentage of boys in a school = 100% – 30% = 70%
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