The Percentage Compendium
Percentage means "per hundred" and denotes a ratio or a fraction as a fraction of 100. It is often denoted using the percent sign, "%". Percentages are used widely in finance, retail, and science to represent proportions, growth, and probability.
The Fundamental Formula
The basic formula for percentage is (Value / Total) × 100 = Percentage. Conversely, to find a value from a percentage, use (Percentage / 100) × Total = Value.
Growth & Decay
Percentage change is used to track the growth or decline of a value over time. It is calculated by dividing the absolute difference by the original value: ((New - Old) / Old) × 100.
Common Equivalents
| Percent | Decimal | Fraction |
|---|---|---|
| 1% | 0.01 | 1/100 |
| 10% | 0.1 | 1/10 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1.0 | 1/1 |
Real-World Applications
Sales tax and discounts are always calculated as percentages of the original price. For example, a 20% discount on a $100 item saves you $20.
Interest rates (APR) represent the cost of borrowing or the return on investment as a percentage of the principal amount.
Polls and survey results are expressed as percentages to represent the proportion of the population that holds a certain view.
Daily recommended intake values and body fat percentages are crucial metrics used in medicine and nutrition.
Pro Tip: Reverse Percentages
Percentages are reversible! 8% of 50 is the same as 50% of 8. Both equal 4. This mental shortcut can make quick estimations significantly easier when the original numbers are complex.