What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning 'out of one hundred.' Percentages are used everywhere — discounts, tax rates, interest rates, exam scores, growth rates, and statistical data. Mastering percentage calculations is one of the most practically useful math skills in everyday life.
3 Types of Percentage Calculations
Type 1: Find X% of a NumberResult = (Percentage ÷ 100) × Number
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
Example: 15% of 200 = (15 ÷ 100) × 200 = 30
Type 2: What Percentage is X of Y?Percentage = (X ÷ Y) × 100
Example: 30 is what % of 200? = (30 ÷ 200) × 100 = 15%
Example: 30 is what % of 200? = (30 ÷ 200) × 100 = 15%
Type 3: Percentage Change (Increase/Decrease)Change % = [(New − Old) ÷ |Old|] × 100
Example: 80 to 100 = [(100 − 80) ÷ 80] × 100 = +25%
Example: 80 to 100 = [(100 − 80) ÷ 80] × 100 = +25%
Common Percentage Examples
| Scenario | Calculation | Answer |
|---|---|---|
| 18% GST on ₹1,000 | 18% of 1000 | ₹180 |
| 20% discount on ₹500 | 20% of 500 | ₹100 off = ₹400 |
| Salary hike from ₹40k to ₹50k | % change | +25% |
| Score 72 out of 90 | (72÷90)×100 | 80% |
| ₹10,000 at 8% interest | 8% of 10000 | ₹800/year |
Percentage vs Percentage Points
These two terms are often confused, especially in news reporting:
- Percentage change: A relative change. If interest rates go from 4% to 6%, that is a 50% increase (2÷4×100).
- Percentage points: An absolute change. Going from 4% to 6% is an increase of 2 percentage points.
💡 When someone says "interest rates increased by 2%," they almost always mean 2 percentage points, not a 2% relative increase. This distinction matters enormously in financial contexts.
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