1. The Core Concepts: Percentage Change
Percentage change measures the relative difference between an old value and a new value. This is critical in business for tracking revenue growth or in academia for tracking performance improvements.
% Change = [(New - Old) / Old] × 100
2. Percentage Points vs. Percent (%)
This is where most people get confused. If an interest rate increases from 10% to 12%:
- It has increased by 2 percentage points.
- It has increased by 20 percent (as 2 is 20% of 10).
Always clarify which term is being used in financial contracts or news reports.
3. Reverse Percentage (Finding the Original)
If you know the discounted price and the discount rate, how do you find the original price? Use this inverse formula:
Original = Final / (1 - Discount %)
Similarly, for finding a price before tax: Original = Price / (1 + Tax Rate).
4. Common Conversions Table
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 1/8 | 0.125 | 12.5% |
| 3/4 | 0.75 | 75% |