Percentage Key Facts Poster
KS3 and GCSEPrintable Reference
Percentage Key Facts Poster
percentages.co.uk
Common Percentage, Fraction and Decimal Equivalents
| Percentage | Fraction | Decimal |
|---|---|---|
| 1% | 1/100 | 0.01 |
| 5% | 1/20 | 0.05 |
| 10% | 1/10 | 0.10 |
| 12.5% | 1/8 | 0.125 |
| 20% | 1/5 | 0.20 |
| 25% | 1/4 | 0.25 |
| 33.3% (recurring) | 1/3 | 0.333... |
| 37.5% | 3/8 | 0.375 |
| 50% | 1/2 | 0.50 |
| 62.5% | 5/8 | 0.625 |
| 66.7% (recurring) | 2/3 | 0.667... |
| 75% | 3/4 | 0.75 |
| 87.5% | 7/8 | 0.875 |
| 100% | 1 whole | 1.00 |
Key Formulas
Percentage of an amount
Amount × (% ÷ 100)
e.g. 30% of 250: 250 × 0.30 = 75
Percentage change
(change ÷ original) × 100
Always divide by the original value
Reverse percentage
new value ÷ multiplier
e.g. after 20% increase: value ÷ 1.20
Compound interest
A = P × (1 + r/100)n
P = principal, r = rate %, n = years
Percentage profit
(profit ÷ cost price) × 100
Always divide by cost price, not selling price
Percentage error
(|approx - exact| ÷ exact) × 100
Always divide by the exact (true) value
Multiplier Quick Reference
To find a multiplier for an increase: (100 + %) ÷ 100. For a decrease: (100 - %) ÷ 100.
Percentage increases
| % increase | Multiplier |
|---|---|
| 1% | × 1.01 |
| 5% | × 1.05 |
| 10% | × 1.10 |
| 15% | × 1.15 |
| 20% | × 1.20 |
| 25% | × 1.25 |
| 30% | × 1.30 |
| 50% | × 1.50 |
| 100% | × 2.00 |
Percentage decreases
| % decrease | Multiplier |
|---|---|
| 1% | × 0.99 |
| 5% | × 0.95 |
| 10% | × 0.90 |
| 15% | × 0.85 |
| 20% | × 0.80 |
| 25% | × 0.75 |
| 30% | × 0.70 |
| 50% | × 0.50 |
Key Vocabulary
| Term | Definition |
|---|---|
| Percentage | A number expressed as a fraction of 100. The symbol % means "per hundred". |
| Per cent | "Per hundred" in Latin. The % symbol literally means ÷ 100. |
| Multiplier | The single decimal number you multiply by to apply a percentage change in one step. For a 15% increase, the multiplier is 1.15. |
| Depreciation | A percentage decrease in the value of an asset over time. Calculated using repeated multiplication by a multiplier less than 1. |
| Compound interest | Interest calculated on the original amount plus all interest already earned. The total grows at an accelerating rate. |
| Simple interest | Interest calculated on the original amount only. The same fixed amount of interest is added each year. |
| Reverse percentage | Finding the original value before a percentage change was applied. Divide the new value by the multiplier. |