# Percentage Formula

The percentage formula is one of the most important formal of Mathematics, it is used to calculate the amount or allocation of something in terms of 100, also used to express a number between 0 and 1, percentage formula is used.

It is represented by the symbol % and is majorly used to compare and find out ratios.

Examples of percentages are:

• 10% is equal to 1/10 fraction
• 50% is equal to 1/2 fraction
• 100% is equal to 1 fraction

To calculate the percentage, the value is divided by the total value and then multiplied the resulting to 100.

Percentage formula = (Value/Total value)×100

## Steps to Calculate Percentage of a Number

Below are the steps followed to calculate the percentage of a number.

Step 1: Identify the actual form of the number, i.e. fraction or decimal. The actual format will define the following mathematical operation on the number. Suppose a decimal number is 0.75, which may be the calculated ratio of the values we are comparing, while an example of a fraction is 21/5.

Step 2: Convert the number into its’s decimal form using mathematical operations. That means, if the given number is a fraction, convert it to a decimal number, else leave it as it is.

Step 3: Multiply the result obtained in the prior step by 100 and the final value should be represented as a percentage.

For example, 0.267 × 100 = 26.7%.

## Steps to Calculate Percentage of Marks

Below are the steps followed to calculate the percentage of marks.

Step 1: Divide the obtained marks by the maximum marks of the exam.

Step 2: Multiply the result by 100.

Example 1: Rahul scored 2115 marks in the college examination out of 2500 marks. Calculate the percentage of marks secured by Rahul.

Solution:

Number of marks scored = 2115

Maximum marks = 2500

Percentage of marks =(2115/2500) × 100

Percentage= 0.846 × 100

Therefore, the percentage of marks secured by Rahul is 84.6%

## Steps to Calculate Percentage Change

Percentage change is the percentage difference between two numbers. The percentage change is the difference in the value of a number or quantity over a period in terms of percentage.

The formula used to calculate Percentage change (Or Percentage difference) is:

% change =[Change in Value / Actual Value] × 100

Here,

Change in Value = New value – Actual value

The change in the value could be both positive and negative.

Based on the nature of change it is classified into two types. They are:

• Percentage increase
• Percentage decrease

## Percentage Increase

Here the new value is greater than the actual value. The percentage change in the value shows the percent increase in the actual number.

Formula:

Percent Increase (% Increase) = (Increase in value/Actual value) × 100

Here, Increase in value = New value – Actual value

### Percentage Decrease

Here the new value is lesser than the actual value. The percentage change in the value shows the percent decrease in the actual number.

Formula:

Percent Decrease (% Decrease) = (Decrease in value/Actual value) × 100

Here, Decrease in value = Actual value – New value

## Percentage Error Formula

There is one more change in a percentage called the percentage error. Normally, this type of error occurs when we deal with weights.

Following is the formula usied to calculate % error

% error = (error × 100) / actual value

## Sample Questions

Question 1: Find 25% of 20.

Solution:

Remember that “of” means “times”

So, Percentage = (25/100) × 20

% = 0.25 × 20 = 5

Therefore, 25% of 20 is 5.

Question 2: There are 200 learners in a class. Out of them, 75 are female. Find the percentage of female learners in the class.

Solution:

Total number of students in the class = 200

Female in the class = 75

% of female learners in the class = (75 ⁄ 200) × 100 = (7500 ⁄ 200) = 37.5%

## Learn Mathematics

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