Content Curator
Percentage is a ratio or a number represented as a fraction of 100, i.e., a fraction with 100 as the denominator. It is represented by the symbol “%”. Percentage simply is parts per 100. For example, if Shreya scored 40% in her maths exam, it means she scored 40 out of 100 marks and that can be expressed as 40/100 in fraction and as 40:100 in ratio.
Percentage is a dimensionless quantity
Read Also: Pair of Linear Equation
| Table of Contents |
Key Terms: Percentage, Percentage Formula, Decimals, Fractions, Percent Change, Percent
Percentage Formula
[Click Here for Sample Questions]
In order to calculate the percentage of a number, follow the below steps:
- Divide the value by the whole value
- Multiply the resultant by 100
The formula to calculate percentage is:
| Percentage = (Value/Total Value) x 100 |
The above formula is used to calculate percentage of a quantity out of the whole quantity.
Let, A is X% of B
Then, according to the above mentioned steps
(A/B) x 100 = X%
| Example: If a student got 20 out 0f 60 marks. What will be his percentage? Solutions: Given total marks is 60 and he got 20 Using the formula, percentage = (20/60) x 100 percentage = 33.34% Percentage of the student is 33.34%. Example: If a student got 120 out 0f 200 marks. What will be his percentage? Solutions: Using the formula, Percentage = (120/200) x 100 = 60% Percentage scored by the student is 60%. Example: If a girl gives away 30 mangoes out of 90 mangoes. What percentage of total mangoes is left with her? Solutions: Remaining number of mangoes is 90 – 30 = 60 Now, using the percentage formula Percentage = (60/90) x 100 Percentage = 66.67% The percentage of mangoes left with the girl is 66.67%. |
Some very commonly used percentages are:
- 10% is equal to 1/10 fraction
- 20% is equivalent to 1/5 fraction
- 25% is equivalent to 1/4 fraction
- 50% is equivalent to 1/2 fraction
- 75% is equivalent to 3/4 fraction
- 90% is equivalent to 9/10 fraction
The video below explains this:
Percentage Error Formula Detailed Video Explanation:
Also Check:
How to Calculate Percentage of a Number?
[Click Here for Sample Questions]
In order to calculate what value is percentage of a number has, follow the below steps:
- Remove the percent “%” sign from the value and divide it by 100
- Multiply the resultant to the total value
Let, A% of B is equal to X
Then, accprding to above mentioned steps
(A/100) x B = X
| Example: What will be 35% of 700? Solutions: According to the formula Total value = 700 Percentage to find = 35% Thus, (35/100) x 700 = 35 x 7 = 245 35% of 700 is 245. |
Percentage Change Formula
[Click Here for Sample Questions]
Whenever the value of a measured quantity changes, the change can be captured through absolute change and percentage change An absolute change is an actual change in the measured quantity and percentage change is the change in percent value.
Percentage change is obtained by the formula:
| (Absolute value Change/ Original quantity) x 100 |
In simple terms, percent change is dividing the difference between old value and new value by the old value and then multiplying the result with 100. An example is given below to understand better.
| Example: If Aman’s salary increased to Rs. 20,000 from Rs. 15,000, what will be the percent change? Solutions: Given that the new salary is Rs. 20,000 while old salary was Rs. 15,000 Change in the salary = New salary – Old salary = 20,000 – 15,000 Change in the salary = Rs. 5,000 = Absolute Value Now, using the formula, percentage Percentage change = (5000/15000) x 100 Percentage change = 33.34% Percentage change in Aman’s salary is 33.34%. |
Applications of Percentage
[Click Here for Sample Questions]
Percentage is used in our day-to-day lives. Some of the important applications of percentage are:
- Percentage is used to compare numerical data and compare data by corporations, firms, government, schools and, colleges.
- Percentage is used by shopkeepers and companies to calculate profit/loss percentage on the goods sold.
- Percentage is used by Banks and financial institutions to calculate interest % on loans, fixed deposit, and savings account.
- Economists also use percentage to calculate the growth rate, inflation rate, and tax rate of a country.
- Percentage is also used to calculate depreciation rate on cars, trucks, and other vehicles.
Also Check:
Fraction to Percent
[Click Here for Sample Questions]
In order to convert a fraction to percent, th efollowing steps must be followed:
- Convert the fraction into decimal number
- Multiply the resultant with 100
To understand better an example is given below:
| Example: Convert 3/4 to a percent. Solution: The decimal form of 3/4 is 0.75 Now, to get the percent we multiply the decimal number by 100 0.75 x 100 = 75% |
Read More: Real Number System
Percentage Chart
[Click Here for Sample Questions]
A percentage chart of fractions into percentage is given below for quick revision of students:
| Fractions | Percentage |
|---|---|
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.66% |
| 1/7 | 14.28% |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/10 | 10% |
| 1/11 | 9.09% |
| 1/12 | 8.33% |
| 1/13 | 7.69% |
| 1/14 | 7.14% |
| 1/15 | 6.66% |
Things to Remember
- Percentage mainly applies to ratios, and the percentage value of a ratio is arrived at by multiplying by 100, the decimal value of a ratio.
- Percentage can be expressed as a decimal and a fraction.
- Percentage is an important and simple tool for the comparison of numerical data and information.
- Whenever the value of a measured quantity changes, the change can be captured through absolute change and percentage change, an absolute change is an actual change in the measured quantity and percentage change is the change in percent value.
- Percentage change is obtained by the formula: (Absolute value Change/ Original quantity) x 100.
Sample Questions
Question: A student scores 20 marks out of a maximum 30 marks. Find the percentage of his marks out of the total marks. [2 marks]
Answer: His marks can then be denoted as 20 out of 30 marks and in percentage is 20/30 * 100 which is equal to 66.66%.
Question: Define percentage. What is formula of percentage? [2 marks]
Answer: Percent means for every 100 and is derived from the French word which means 100.Percentage mainly applies to ratios, and the percentage value of a ratio is arrived at by multiplying by 100, the decimal value of a ratio. The formula of Percentage is:
Percentage = (Value/Total Value) * 100.
Question: What is the 60 % of 300? [2 marks]
Answer: 60 % of 300 is (60/100)* 300 is 180.
Question: What percentage is 30 of 120? [3 marks]
Answer: The formula of Percentage is:
Percentage = (Value/Total Value) * 100.
Here, Value = 30 and Total Value = 120.
So, percentage is (30/120) * 100 = 25%.
Question: A shopkeeper sells a pen whose cost price is Rs 15 and sales price is Rs 20. The profit is Rs 5. Find the profit percentage. [3 marks]
Answer: The formula of Percentage is:
Percentage = (Value/Total Value) * 100
Percentage = (Value/Total Value) * 100.
The profit percentage of the shopkeeper is (5/15)* 100 which is equal to 33.33%.
Question: The salary of a person is Rs 1200 and the savings is Rs 300. Find the saving percentage? [2 marks]
Answer: The formula of Percentage is:
Percentage = (Value/Total Value) * 100
Here Value = Rs 300 and Total Value = Rs 1200
Saving Percentage is (300/1200)* 100 is 25 %.
Question: The salary of a person is Rs 1200 and the savings is Rs 300. Find the expenditure percentage? [3 marks]
Answer: Expenditure = Salary – Savings
= 1200 – 300
= 900
The formula of Percentage is:
Percentage = (Value/Total Value) * 100
Here Value = Rs 900 and Total Value = Rs 1200
Saving Percentage is (900/1200)* 100 is 75 %.
Question: If 10% of a is 40. Find a. [2 marks]
Answer: 10 % of a = 40
10a/100 = 40
a = 400.
Question: Find the interest on Rs 800 if the interest rate is 10%? [2 marks]
Answer: Interest = Rs 800 and Interest Rate = 10%
Interest Amount = (800*10)/100 is Rs 80.
Question: What will be the value of 175% of 100? [2 marks]
Answer: 175% of 100 = (175/100) x 100 = 175
Hence, 175% of 100 will be 175.
Also Read:
Comments