In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
Examples of percentages are:
- 10% is equal to 1/10 fraction
- 20% is equivalent to ⅕ fraction
- 25% is equivalent to ¼ fraction
- 50% is equivalent to ½ fraction
- 75% is equivalent to ¾ fraction
- 90% is equivalent to 9/10 fraction
Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.
Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc. In academics, the marks obtained in any subject are calculated in terms of percentage. Like, Ram has got 78% of marks in his final exam. So, this percentage is calculated on account of the total marks obtained by Ram, in all subjects to the total marks.
Percentage Formula
To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
Percentage formula = (Value/Total value) × 100
Example: 2/5 × 100 = 0.4 × 100 = 40 per cent
How to calculate the percentage of a number?
To calculate the percentage of a number, we need to use a different formula such as:
P% of Number = X
where X is the required percentage.
If we remove the % sign, then we need to express the above formulas as;
P/100 * Number = X
Example: Calculate 10% of 80.
Let 10% of 80 = X
10/100 * 80 = X
X = 8
Percentage Increase and Decrease
The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
% increase = [(New number – Original number)/Original number] x 100
where,increase in number = New number – original number
Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100.
% decrease = [(Original number – New number)/Original number] x 100
Where decrease in number = Original number – New number
So basically if the answer is negative then there is a percentage decrease.
Solved Example
Two quantities are generally expressed on the basis of their ratios. Here, let us understand the concepts of percentage through a few examples in a much better way.
| Example: Let a bag contain 2 kg of apples and 3kg of grapes. Find the ratio of quantities present, and the percentage occupied by each. Solution: The number of apples and grapes in a bag can be compared in terms of their ratio, i.e. 2:3. The actual interpretation of percentages can be understood as follows: The same quantity can be represented in terms of the percentage occupied, which can be done as given below. Total quantity present = 5 kg Ratio of apples (in terms of total quantity) = 2/5 From the definition of percentage, it is the ratio that is expressed per hundred, (1/100) = 1% Thus, Percentage of Apples = (2/5) × 100 = 40% Percentage of Grapes = (3/5) × 100 = 60% Percentage ChartThe percentage chart is given here for fractions converted into percentages. |
