Percentage

Definition of Percentage

The Concept of percentage is used to measure the proportion of value in terms of the original value. Percentages are widely used in business for computing profit or loss percentage of a business. Also it is used in schools and colleges to represent the marks obtained by the students. Marks of the students can be estimated using a percentage formula. Percentages are generally defined as a ratio of any value to the whole value multiplied by 100. The symbol used to represent the percentage is %.


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Percentage Meaning

Percentage means a number or a ratio represented in the form of fractions of 100. It is represented using the percentage sign ‘%’. The abbreviations used to represent the percentage are ‘pct’ or ‘pc’. In other words, the percentage is defined as how much of one quantity is made by another quantity and it is evaluated in terms of 100.


The percentage has no dimensions. It means they are dimensionless numbers. If we say 60% of a number, then it implies 60 percent of its whole. It can even be expressed in both decimal and fraction forms such as 0.56% or 0.87%. In the examination, marks scored by students in any subject are calculated with respect to the percentage. For example-Pooja scored 78% of marks in his exam. So, this percentage is calculated in terms of total marks obtained by Pooja in all the subjects to the total maximum marks and then the result will be multiplied by 100.


Percentage Definition

The Percentage is a relative value that indicates hundredth parts of any quantity. One percent (1%) represents the one hundredth, 2 percent (2%) represents two hundredths, 100% represents the whole, 200% twice the given quantity and so on…


For example - 1 percent of 1000 mangoes is equal to 1/100 of 1000 or 10 mangoes.


Percentage in Maths

Each percentage problem has three possible unknown or variables. These unknown or variables are

  • The percent

  • The part

  • The base


To solve the percentage problem, you need to recognize these unknown variables


For Example

  1. 70% of 40 is 28

Here,

70 is the percent

40 is the base

28 is the part


  1. 6 is 50% of 12

Here, 

6 is the part

50 is the percent

12 is the base


Basic Percentage Trick

The following trick can be used to calculate the percentage:


X % of y= y % of x


Example: Prove 10% of 50 is equal to 50% of 10

Solution : 10% of 50 = 5

50% of 10 = 5

Hence, they are equal i.e. x % of y = y % of x holds true.


Percentage Formula

We should know the percentage formulas to calculate the percentages. The basic formula used to calculate the percentage is equal to the ratio of actual value to the total value and multiply it by 100. The formula of the percentages expressed as


Percentage % = \[\frac{\text{(Actual value)}}{\text{Total value}}* 100\]


Percentage Formula in Case of a Fraction


\[\frac{\text{Numerator}}{\text{Denominator}} * 100\]


Percentage Change Formula

\[\text{Percentage change} = \frac{\text{(New value - Original value)}}{\text{Original value}} *100\]


Percentage Increases Formula

When the new value is greater than the original value. The percentage change in the value signifies the percentage increase in the original number such that,

Percentage Increase (% Increase) = \[\frac{\text{Increase in value}}{\text{original value}}\] * 100


Here, Increase in value = New value – original value.


Percentage Decreases Formula

When the new value is lesser than the original value. The percentage change in the value signifies the percentage decrease in the original number such that,

Percentage Decrease (% Decrease) = \[\frac{\text{Decrease in value}}{\text{original value}}\] * 100


Here, Decrease in value = Original value - New value


How to Calculate the Percentage of a Number

We need to use some formula to calculate the percentage of a number. The formula which is to be used is:


P% of a number = X

Where x is the required percentage


If the percentage sign is removed, then the above formula is expressed as


\[\frac{P}{100}\] * Number= X


For example:

Calculate 20 % * of 800

Let 20 % * of 800 = X

\[\frac{20}{100}*800\] = X

X = 160


Solved Example

1. In a class of 70 students, 60% are boys. Find the total number of girls and boys in the class?


Solution: Total number of boys in class = 60% of 70

= \[\frac{60}{100}\] * 70

= 0.6 * 70

= 42

Total number of girls in the class = Total number of students in the class - Number of boys

= 70 - 42

= 28

Hence, the numbers of boys in the class are 42 and the number of girls in the class is 28.


2. What is 70% of 800?


Solution: 70% of 800

= \[\frac{70}{100}\] * 800

= \[\frac{(70 *800)}{100}\]

= \[\frac{56000}{100}\]

= 560


3. Ķrita scored 92% marks in examinations. If these are 460 marks, calculate the maximum marks.


Solution: Let maximum marks be X

Then 92% of X= 460

\[\frac{92}{100}\] * X = 460

X = \[\frac{(460 *100)}{92}\]

X = \[\frac{46000}{92}\]

X = 500

Hence, the maximum marks in the examination are 500.


4.  The annual salary of Karan was increased from Rs. 18, 00,000, to Rs. 22, 00,000. Calculate the percentage increase.


Solution:

Original salary of Karan = Rs. 18, 00,000

Increased salary of Karan = Rs. 22, 00,000

Increase in Salary = Rs. 22,00,000 - 18, 00,000= Rs. 4, 00,000

Hence, the percentage increase in salary = \[\frac{\text{Increase in salary}}{\text{original salary}}\]* 100

\[\frac{4,00,000}{18, 00,000}\times 100\] = 22.2%


Fun Facts

  • The concept of percentage was not developed by any person. The percentage concept originated throughout History. In Ancient Rome, mathematical calculations were expressed in fraction of 100. This concept was later originated in Percentage.


Quiz Time

1. Half percentage written as a decimal is

  1. 0.2

  2. 0.02

  3. 0.005

  4. 0.05


2. 1.14 expressed as a percent of 1.19 is

  1. 6

  2. 10

  3. 60

  4. 90


3. What is 30% of 80?

  1. 20

  2. 24

  3. 56

  4. 78

FAQ (Frequently Asked Questions)

1. How to Calculate the Percentage of a Decimal Number, Fraction Form and Percentage of Marks?

Method to calculate  the percentage of a decimal number and Fraction form are:


Generally, the numbers that are to be converted in percentages are given in two forms. These two forms are Decimal form and Fraction form.


Decimal Form – If the given number is in decimal form, then it will be easy to find the percentage. To get the percentage, the given number will be multiplied by 100. For example- the given number is 0.55. To convert into a percentage, 0.55 *100 = 55%


Fraction Form - If the given number is in fraction form, then the first step is to convert into the decimal value by dividing the upper value by total value and then the result will be  multiplied with 100. For example -1/4 will be converted in percentage as ¼ *100= 0.25 *100 = 25%.


Method to calculate the  percentage of Marks

A percentage is a number that is represented as a fraction of 100.  The method to calculate the percentage of marks is explained here in detail.


To find the percentage of marks, divide the total marks of a particular student in all the subjects to the total maximum marks and then multiply the result with 100.


For example- If the total marks scored in the examination are 600 out of 800 then the percentage of marks will be calculated as


Percentage of marks = (600/800)* 100

Percentage - 0.75 *100 = 75%

Hence, the percentage of marks optioned is 75%

Percentage of marks, numbers can easily be found using the percentage formulas.