Percentage — How to Calculate It with Easy Examples
Key Points At A Glance
- Percentage means "out of 100" and uses the symbol %.
- To find a percentage, use (Part ÷ Whole) × 100.
- To find a percentage of a number, use (Percentage ÷ 100) × Number.
- A quick trick: 10% of a number is found by moving the decimal one place left.
- Fractions, decimals and percentages are different ways to write the same value.
- Percentages are used in marks, discounts, bank interest and statistics.
You see percentages everywhere — exam marks, shop discounts, phone battery, loan interest. Understanding them is one of the most useful maths skills in real life. The good news is that percentages are simple once you learn one basic idea. Let's master them step by step.
What Is a Percentage?
The word percentage comes from "per cent", which means "out of 100". A percentage is just a way of expressing a number as a part of 100.
- The symbol for percentage is %.
- So 25% simply means 25 out of 100, or 25/100.
This is why percentages make comparison easy — everything is measured against the same base of 100.
The Basic Percentage Formula
To find what percentage one number is of another, use:
- Percentage = (Part ÷ Whole) × 100
Example: You scored 40 marks out of 50. What is your percentage?
- (40 ÷ 50) × 100 = 0.8 × 100 = 80%
Finding a Percentage of a Number
This is the most common everyday calculation. The formula is:
- (Percentage ÷ 100) × Number
Example: Find 20% of 150.
- (20 ÷ 100) × 150 = 0.2 × 150 = 30
Converting Between Fractions, Decimals and Percentages
These three are just different ways of writing the same value:
- Fraction to percentage: multiply by 100. ½ = (1÷2) × 100 = 50%.
- Decimal to percentage: multiply by 100. 0.75 = 75%.
- Percentage to decimal: divide by 100. 60% = 0.6.
Percentage Increase and Decrease
This is useful for prices, marks and growth.
- Increase: new value goes up. If a ₹200 item rises by 10%, the increase is (10÷100) × 200 = ₹20, so the new price is ₹220.
- Decrease (discount): value goes down. If a ₹500 item has a 20% discount, the discount is (20÷100) × 500 = ₹100, so you pay ₹400.
Real-Life Uses of Percentage
- Exam results — your marks are shown as a percentage.
- Shopping discounts — "30% off" sales.
- Bank interest — on savings and loans.
- Statistics and news — "70% of people prefer…".
Common Mistakes to Avoid
- Forgetting to multiply by 100 when finding a percentage.
- Mixing up the part and the whole in the formula.
- Forgetting to add or subtract the change for increase/decrease problems.
Quick Summary
- Percentage means "out of 100" and uses the symbol %.
- To find a percentage: (Part ÷ Whole) × 100.
- To find a percentage of a number: (Percentage ÷ 100) × Number.
- Percentages are used in marks, discounts, interest and statistics.
Percentages get easy with practice, so try working out a few discounts the next time you shop. They connect closely to fractions, so our Fractions Made Easy notes are a great companion. To revise efficiently before exams, use How to Study Smart for Exams, and explore more Mathematics notes and all our study notes any time.
Frequently Asked Questions
A percentage is a way of expressing a number as a part of 100. The symbol % means "out of 100", so 25% means 25 out of 100.
To find what percentage one number is of another, use the formula (Part ÷ Whole) × 100. For example, 40 out of 50 is (40 ÷ 50) × 100 = 80%.
Use the formula (Percentage ÷ 100) × Number. For example, 20% of 150 is (20 ÷ 100) × 150 = 30.
Divide the fraction and multiply the result by 100. For example, ½ becomes (1 ÷ 2) × 100 = 50%.
Find the percentage of the price, then subtract it. For a 20% discount on ₹500, the discount is (20 ÷ 100) × 500 = ₹100, so you pay ₹400.
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