Before knowing about how to calculate a percentage, let us know what a percentage is. In this article, we will discuss in detail what is a percentage, how to calculate the percent increase and decrease, how to estimate the percent of a number using the percentage formula, with examples. The topics related to percentage have been introduced to the students in Class 7 and Class 8 syllabus.
The concept of percentage is used to measure the tendency of value with respect to the original value. This has a huge application in business while computing profit and loss percentage. Also, in schools and colleges, the marks obtained by the students are estimated with the percentage formula. Percentage basically defines the ratio of any value to a whole value multiplied by 100. The symbol used to denote percent is “%”. Let us learn how to calculate the per-cent value.
Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”. The abbreviation used to represent the percentage is “pct” or “pc”. In other words, the percent or the percentage is defined as how much of one quantity is made by the other quantity and it is evaluated in relation to 100.
Now, to calculate the percentage we have to know its formula. The formula to calculate percentage is equal to the ratio of the actual value to the total value multiplied by 100. The percentage formula is:
Percentage, % = (Value × 100) / Total Value
Let us understand this concept and formula with the help of an illustrative example given below:
Example: A circle is given below with 10 divisions and few parts are shaded. Calculate the percentage of shaded parts in the circle.
Total number of divisions in the circle = 10
Number of shaded parts = 2
We know that,
Percentage, % = (Value × 100) / Total Value
Thus, the percentage of the shaded part of the circle = [(Number of shaded divisions)/ (Total number of divisions)] × 100
= (2/10) × 100
Some other important percentage formulas are:
- Percentage change formula
- Percent Increase
- Percent Decrease
- Percentage error formula
Percentage Change Formula
% change = ((New value – Original Value) × 100) / Original Value
There are two different types of percentage change. They are
- Percentage Increase
- Percentage Decrease
When the new value is greater than the original value, then the percentage change in the value shows the percent increased in the original number. This can be calculated as:
Percent Increase (% Increase) = (Increase in Value/Original Value) x 100
Increase in Value = New Value – Original Value
When the new value is lesser than the original value, then the percentage change in the value shows the percent decrease in the original number. The formula for percentage increase is given by:
Percent Decrease (% Decrease) = (Decrease in Value/Original Value) x 100
Decrease in Value = Original Value – New Value
Also check: Percentage Increase and Decrease
Percentage Error Formula
% error = (error × 100) / real value
How to calculate the Percentage of a Number
Generally, the numbers that are converting into the percentage are given in two formats.
- Decimal form – If the number is given in decimal format, it is easy to find the percentage. To obtain the percentage, multiply the given number by 100. For example, the given number is 0.45. To convert into a percentage, 0.45 * 100 = 45%
- Fraction form: If the number is given in fractional format, first convert into decimal value by dividing the top value by the total value and then multiply with 100.
By using percentage formulas, it is easy to know how to calculate the percentage of marks, discounts, etc.
How to calculate Percentage of Marks
A percentage is a number that is expressed as a fraction of 100. Here, how to calculate the percentage of marks is explained in detail.
To find the percentage of the marks, divide the marks obtained in the examination with the maximum marks and multiply the result with 100.
Example 1: If 1156 is the total score obtained in the examination out of 1200 marks, then divide 1156 by 1200, and then multiply it by 100.
It means that,
Percentage of marks =(1156/1200) x 100
Percentage= 0.9633 x 100
Therefore, the percentage of marks obtained is 96.3%
Difference Between Percentage and Percentile
In most of the cases, many people might get confused with percentage and percentile. Both are different. Here, the difference between percentage and percentile is given in detail.
|The percentage represents the number out of 100||Percentile is not a number out of 100|
|It can be written as ratios or proportions||It cannot be written as ratios or proportions|
|A percentage is obtained by multiplying the ratio of two numbers with 100||A percentile is a percentage of values that can be found below a specific value|
|It is not based on ranking numbers||It is based on ranking numbers|
|It is written in the form of x%||It is written in the form of xth|
|It is based on one case||Comparison of one case with other|
|It does not rely on the normal distribution||It relies on the normal distribution|
Also, read: Difference Between Percentage And Percentile
Calculating Percentage Examples
Question 1: There are 120 students in a class. Out of them, 60 students are boys. Find the percentage of boys in the class.
Total number of students in class = 120
Number of boys in class = 60
Therefore, the percentage of boys in class = ( 60 × 100)/120
= 600/12 = 50
So, the percentage of boys in class = 50%
Question 2: Find 25 % of 10.
Remember that “of” means “times”
So, Percentage = (25/100) × 10
% = 0.25 × 10 = 2.5
Therefore, 25% of 10 is 2.5.
Question 3: Find the percentage of the ripened apples, if the number of ripe apples is 10 and the total number of apples in the basket are 60.
Solution: Given, the total number of apples = 60
Number of ripe apples = 10
Percentage of ripe apples = (10/60) × 100
= (1/6) × 100
Question 4: There are 150 people present in a cinema hall. The number of men are 80 and the number of women is 70 in the hall. Calculate the percentage of men present in the hall.
Solution: Total number of people present in cinema hall = 150
Number of men = 80
Percentage of men = (80 x 100)/150
Question 5: What is 15% of 75 equal to?
Solution: 15% of 75 = (15/100) × 75 = 11.25
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