Percentage: Meaning, Formula, Solved Examples

Percentage: A percentage is a mathematical term that implies a component per hundred. The word  percentage comes from the Latin phrase “per centum,” which simply translates as “by hundred.” Percentages have a denominator of 100 and are fractions. To find the percent of a number, divide it by the whole number and multiply by 100. In this article, we have discussed everything about percentages like how to calculate, percentage formula, percentage calculator, percentage chart, etc.

Moreover, it is well known that the percentage has no dimension. In technical terms, a percentage is also known as a dimensionless number. Students’ grades in any subject are expressed as a percentage during the examination. In this article, we will go over percentages in detail, including how to calculate them, formulas, and more.

What is Percentage Meaning?

A percentage is a number or ratio expressed as a fraction of \(100\). The word percentage means per \(100\) and it is represented by the symbol \(\% \). The percentage is defined as part or amount in every \(100\). Percentages can also be represented in decimal or fraction form such as \(0.3\% ,0.75\% \) etc.

Percentage Calculator Formula

The word percentage came from per cent. So, if you split the word percentage, you will get Per and Cent. Cent is an old European word that means “Hundred”. 
Let us understand how to calculate or find the Percentage by using the percentage calculator formula:
To calculate percent of a number, divide the number by whole and multiply it by \(100\).

Percentage \( = \frac{{{\rm{Actual}}\,{\rm{number}}}}{{{\rm{Total}}\,{\rm{number}}}} \times 100\% \)

\(p = \frac{x}{y} \times 100\% \)

Here,

\(x\) – Actual number

\(y\) – Total number

\(p\) – Percentage

Percentage Calculator Online

Example: Find the Percentage of marks obtained by Keerthi in Maths, where Keerthi has secured  \(90\) marks out of \(100\).
The Percentage obtained by Keerthi  can be calculated as follows:
\(\frac{{90}}{{100}} \times 100\%  = 90\% \)

Percentage Difference Between Two Numbers

The percentage difference for any two numbers can be calculated using the formula: 

\({\text{percentage}}\,{\text{difference=}}\frac{{{\text{Absolute}}\,{\text{difference}}\,{\text{of}}\,{\text{two}}\,{\text{numbers}}\,}}{{{\text{Average}}\,{\text{of}}\,{\text{two}}\,{\text{numbers}}}}\)

Let us consider two numbers \(x\) and \(y\), Percentage difference  \(= \frac{{|x – y|}}{{\frac{{\mid x – y}}{2}}}\)
Here, \(|x – y|\) is the absolute difference between two numbers.
\(\frac{{x + y}}{2}\) is the average of two numbers.

We have the formula to show the change in quantity as a percentage. Two cases might arise while calculating percentage difference and they are:

1. Calculate Percentage Increase 
2. Calculate Percentage Decrease

Formula for Percentage Increase

Percentage increase refers to the percentage change in the value when it is increased over a period of time.
For example, population increase, increase in the number of bacteria on a surface, etc.
Percentage increase can be calculated by using the following formula:

\({\text{Percentage}}\,{\text{Increase=}}\frac{{{\text{Increased}}\,{\text{value-Original}}\,{\text{value}}\,}}{{{\text{Original}}\,{\text{value}}\,}}{{ \times 100}}\)

Formula for Percentage Decrease

Percentage decrease refers to the percentage change in the value when it is decreased over a period of time.
For example, a decrease in the level of rainfall, a decrease in the number of patients in the hospital, etc.
Percentage decrease can be calculated by using the following formula:

\({\rm{Percentage \; Decrease = }}\frac{{{\rm{ Original value – Decreased value }}}}{{{\rm{ Original value }}}}{\rm{ \times 100\% }}\)

Parts of Percentage: Percentage of a Number

Before calculating the Percentage of a Number, we need to know about the parts of the it. Every problem of Percentage has three parts or variables, which helps you solve the problem easily. They are

1. Percentage
2. Base
3. Part

Look at the below example:

Example: \(25\% \) of \(200\) is\(50\).

Here, \(25\) is the Percentage.

\(200\) is the base.

\(50\) is the part.

Conversion of Fraction To Percent

To convert the given fraction to a percent, we should multiply it by a hundred.

Let us consider a fraction \(\frac{{\rm{x}}}{{\rm{y}}}\).

Multiply and divide the given fraction by \({\rm{100}}\).

So, we shall write \(\frac{{\rm{x}}}{{\rm{y}}}\) as  \(\frac{{\rm{x}}}{{\rm{y}}}{\rm{ \times }}\frac{{{\rm{100}}}}{{{\rm{100}}}}\)

We know that, according to the definition of Percentage, \(\frac{{\rm{1}}}{{{\rm{100}}}}{\rm{ = \% }}\)

So we shall write \(\frac{x}{y} \times \frac{{100}}{{100}}\) as \(\frac{x}{y} \times 100\% \)

To convert the fraction to a percentage value, multiply it with \({\rm{100}}\).

\({\rm{Fraction \times 100\% }}\)

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Percentage Chart

Below we have provided a percentage chart for your reference:

Ratio and Percentage

To convert the ratio of two numbers \(a:b\) in Percentage, write the given ratio in the fraction form and multiply it with hundred.

\((a:b) = \left( {\frac{a}{b}} \right) \times 100\% \)

Percentage Profit and Loss

Selling price is the price at which a commodity is sold, and cost price is the price at which the commodity was bought originally.

In the case of profit, the selling price is more than the cost price. So, profit is the difference between the selling price of a commodity and the cost price. 

Profits (and losses) are usually depicted in the form of profit percent to describe how much profit or loss a business/individual gets.

Profit = Selling price – cost price.

Profit percentage is given by \({\rm{\% Profit = }}\frac{{{\rm{ Profit }}}}{{{\rm{ Cost price }}}}{\rm{ \times 100\% }}\)

Similarly, in the case of loss, the selling price is less than the cost price.

We know that Loss \( = \) cost price \( – \) selling price.

Loss percentage is given by \({\text{% Loss=}}\frac{{{\text{Loss}}}}{{{\text{Costprice}}}}{\text{ 100% }}\)

How to Calculate Percentage of Marks?

If you are looking for how to calculate the percentage of marks, check out here. To calculate the percentage of marks secured by a student in an examination, you must divide the total marks secured by the student (in all subjects) by the maximum marks and then multiply it by\(100\).

\({\text{Percentage=}}\frac{{{\text{Marks}}\,{\text{obtained}}\,{\text{in}}\,{\text{all}}\,{\text{subjects}}}}{{{\text{Maximum}}\,{\text{marks}}\,{\text{in}}\,{\text{all}}\,{\text{subjects}}}}\) \( \times {\text{100}}\)

For example, if a student has secured \(95\) out of \(100\) in Maths, \(85\) out of \(100\) in Physics, and \(75\) out of \(100\) in Chemistry.
The total marks secured by the student is \((95 + 85 + 75) = 255\)
Maximum marks is \({\rm{(100 + 100 + 100) = 300}}{\rm{.}}\)

Therefore, the Percentage of marks obtained by the student is
\(\left( {\frac{{255}}{{300}}} \right) \times 100\%  = 85\% \)

How to Calculate Percentage Error?

Percentage Error is the difference between approximate (or observed) value and exact (or actual value) as a percentage of actual value.
It is used for purposes such as checking manufacturing or calibration errors in measuring instruments, etc.

\({\text{Percentage=}}\frac{{{\text{Marks}}\,{\text{obtained}}\,{\text{in}}\,{\text{all}}\,{\text{subjects}}}}{{{\text{Maximum}}\,{\text{marks}}\,{\text{in}}\,{\text{all}}\,{\text{subjects}}}}\) \( \times {\text{100}}\)

How to Calculate Percentile?

Many people might confuse Percentage with percentile. However, these two terms are very different. Percentage denotes a number out of \(100\), but percentile does not denote any number. Percentile cannot be expressed as ratios or proportions like a percentage.

Percentile formula is used to ascertain the performance of a person with respect to others. This formula is often used in exam results and scores to denote the individual performance of a candidate with reference to others. The percentile formula is also used to calculate income, weight, etc. 

So, for a value \({‘x’}\), its percentile can be expressed as the ratio of the number of denominations below \({‘x’}\) to the total number of denominations.

\({\text{Percentile=}}\frac{{{\text{Number}}\,{\text{of}}\,{\text{deno}}\,{\text{min}}\,{\text{ations}}\,{\text{below}}{\,^{\text{‘}}}{{\text{x}}^{\text{‘}}}{\text{ 100}}}}{{{\text{Total}}\,{\text{number}}\,{\text{of}}\,{\text{deno}}\,{\text{min}}\,{\text{ations}}}}\)

Solved Examples

Question 1: Let us say you have joined a company and your salary is supposed to be \({\rm{Rs}}{\rm{.40,000}}\). But you later realize that there will be a deduction of \(5\% \) from your salary. So, how much you will be getting paid?

Answer:

1. You need to find \({\rm{5\% }}\) of \({\rm{Rs}}{\rm{.40,000 = }}\left( {\frac{{\rm{5}}}{{{\rm{100}}}}} \right){\rm{ \times 40,000 = Rs}}{\rm{.2000}}\)
2. So, there will be a deduction of \({\rm{Rs}}{\rm{.2000}}{\rm{.}}\).
3. Subtract \({\rm{Rs}}{\rm{.2000}}{\rm{.}}\) from \({\rm{Rs}}{\rm{.40,000}}\) and that will give you \({\rm{Rs}}{\rm{. 38000 }}{\rm{.}}\)
4. So, \({\rm{Rs}}{\rm{. 38000 }}{\rm{.}}\) is the salary that you will be getting in hand

Question 2: Assume that you bought a shirt whose price is \({\text{Rs}}\,\,599\). But there is a \(5\% \) GST. How to know what you need to pay at the bill counter.

Answer:

1. Find \(5\% \) of \( = {\text{Rs}}.599\) and that will give \( = 5\% \times 599 = \frac{{\left( 5 \right)}}{{100}} \times 2995 = {\text{Rs}}.29.95\)
2. So, \({\rm{Rs}}{\rm{.29}}{\rm{.95}}\) is the extra amount that you need to pay at the counter.
3. Add \({\rm{Rs}}{\rm{.599}}\)and \(29.95 = 599 + 29.95 = 628.95.\).
4. So, you need to pay \({\rm{Rs}}{\rm{. 629}}\) at the counter.

Question 3 Assume that you are watching an advertisement and it says that there is a \(20\% \) discount on a laptop. The price tag after the discount as \({\text{Rs}}\,\,55,000\). Figure out how much was the real price.

Answer:

Here, we have the following information: Discount given: \(20\% \) and price after discount:\(= {\text{Rs}}.55000\)

Let us assume that the actual price of the laptop is \( = {\text{Rs}}\,{\text{x}}\).

Therefore, \( {\text{=}} { {\text{R}}_ {\text{s}}} {\text{x-}}\left({{\text{20% }}\, {\text{of}}\, {\text{Rs}} {\text{.X}}} \right) = { {\text{R}}_ { {\text{s}}{\text{.}}}}\,55000\)

\({\text{=Rs}}{\text{.X-Rs}}{\text{.}}\frac{{\left({20} \right)}}{{100}} \times X = {\text{Rs}}.55000\)

\( \Rightarrow {\text{Rs}}{\text{.X-Rs}}{\text{.}}\frac{{\left( X \right)}}{5} = {\text{Rs}}.55000\)

\( \Rightarrow {\text{Rs}}{\text{.}}\frac{{\left({4X} \right)}}{5} = {\text{Rs}}55000\)

\({\text{X=Rs}}{\text{.}}\frac{{55000 \times 5}}{4} = {\text{Rs}}{\text{.687}}50\)

Question 4: Assume that you are appearing for the final examination in which you have already scored \({\rm{Rs}}{\rm{.567}}\) marks out of the last \(6\) papers. Only \(1\) paper is left which is of \(100\) marks. And you have to score in this paper such a way that your average Percentage is at least \(95\% .\) How much should you score at least?

Answer:

In \(6\) last papers, your score is \(567\) marks.
Your target is \(95\% \).

\(95\% \) of \(7\) papers in marks will be \(\frac{{95}}{{100}} \times \)Total marks in \(7\) papers.

\(\left( {\frac{{95}}{{100}}} \right) \times 700 = 665\) Marks

Marks obtained in \(6\) papers is \(665\) Marks \( – 567\) Marks \(= 98\) Marks.

Question 5: In \({\bf{2010}}\), the population of India was at \({\bf{1}},{\bf{234}},{\bf{281}},{\bf{170}}\) people. In \({\rm{2019 ,}}\), the population was recorded at \(1,366,417,754\) people. How much is the percentage change after \(9\) years?

Answer:

Using,  \({\rm{PercentageIncrease = }}\frac{{{\rm{ Increased valus – Original value }}}}{{{\rm{ Original value }}}} \times 100\)

 \(= \left( {\frac{{1,366,417,754 – 1,234,281,170}}{{1,234,281,170}}} \right) \times 100\)

\( = 10.7055\% \)

So, there was a \( = 10.7055\% \) increase in the population of India after \(9\) years.

Question 6: A person says that in a year, it snowed \(13\) days. What is the percentage of days that year during which it snowed?

Answer:

We need to know first that there is a total of \(365\) days in a year (assuming that it is not a leap year). There are given \(13\) snowed days.

The required Percentage is given by \(\frac{{13}}{{365}} \times 100 = 3.5\% \)

Also, refer,

Summary

The percentage is defined as a number or ratio expressed as a fraction of 100. The percentage is denoted by \(\% \). Percentage change is defined as an increase or decrease from the previous value. Percentage decrease is defined as the percentage change in the value when it is decreased with time. Percentage increase can be described as the percentage change in the value when it is increased with time.

Furthermore, percentage can be calculated with the help of the formula given below:
\( {\text{Percentage=}}\frac{{{\text{Actual}}\,{\text{number}}}}{{{\text{Total}}\,{\text{number}}}} \times {\text{100}}\)

FAQs on Percentage

Q.1: What is the symbol of percentage?
Ans: Percentage is denoted by the symbol \(\% \).

Q.2: How to calculate percentage change?
Ans: Percentage change is either increase or decrease from the previous value. If the new value is more than the previous value, then there is a Percentage Increase. If the new value is less than the previous value, then there is a Percentage Decrease. The formula for percentage change is given below:

\({\rm{Percentage Change = }}\left( {\frac{{{\rm{ New Value –  Old Value }}}}{{{\rm{ Old Value }}}}} \right){\rm{ \times 100}}\)

Q.3: What does percentage mean?
Ans: Percentage means per hundred, which can be written in maths as \(\frac{1}{{100}}.\)

Q.4: How do I calculate a percentage?
Ans: Percentage of a number can be calculated by using the formula:
\( {\text{Percentage=}}\frac{{{\text{Actual}}\,{\text{number}}}}{{{\text{Total}}\,{\text{number}}}} \times {\text{100}}\)

Q.5: What is \(40\% \) of \(120\)?
Ans: To calculate the \(40\% \) of \(120\) the students can follow the below-mentioned steps: \(40\% \) of \(120\)
\( = \frac{{40}}{{100}} \times 120 = 48\)

Q.6: How to calculate the total percentage of marks?
Ans: To calculate the percentage of marks secured by a student in an exam, you have to divide the total marks secured by the student (in all subjects) by the maximum marks and then multiply it by 100.

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We hope this detailed article on Percentage helped you in your studies. If you have any doubts or queries regarding this, feel to ask us in the comment section and we will answer you at the earliest.