Percentages Made Easy
Discounts, tips, test scores, interest rates: percentages are everywhere. Four short lessons take you from “what does % mean?” to working them out in your head.
What a percent really is
“Percent” means per hundred. 25% is 25 out of every 100, the same as the fraction 25/100 or the decimal 0.25.
To turn a percent into a decimal, divide by 100: move the decimal point two places left.
| Percent | Decimal | Fraction | Think of it as |
|---|---|---|---|
| 50% | 0.5 | 1/2 | half |
| 25% | 0.25 | 1/4 | a quarter |
| 10% | 0.1 | 1/10 | a tenth |
| 1% | 0.01 | 1/100 | a hundredth |
| 200% | 2 | 2/1 | double |
Over 100% is fine. 150% just means one and a half times the original amount.
Finding a percent of a number
- 20% as a decimal is 0.20
- 0.20 × 85 = 17
- 20% of 85 is 17
Do it in your head with the 10% trick. To find 10%, move the decimal point one place left. Everything else builds from that.
- 10% of 85 = 8.5
- 5% is half of that = 4.25
- 20% is double = 17
- 15% is 10% + 5% = 12.75
Handy flip: x% of y is the same as y% of x. 8% of 50 is hard; 50% of 8 is 4. Same answer.
Percent increase and decrease
- Change: 1,320 − 1,200 = 120
- Divide by the old value: 120 ÷ 1,200 = 0.1
- × 100 = 10
- A 10% increase
Watch out: a 50% drop followed by a 50% rise does not get you back to where you started. $100 → $50 → $75. The second change is a percent of a smaller number.
Percent vs percentage points: if an interest rate goes from 4% to 5%, that's a rise of 1 percentage point, but a 25% increase in the rate itself.
Discounts, tax and tips
The quickest way to apply a percent change is to multiply by a single number:
- 30% off: you pay 70%, so multiply by 0.70.
- 8% tax on top: you pay 108%, so multiply by 1.08.
- 18% tip: multiply the bill by 0.18 for the tip, or by 1.18 for the total.
Stacked discounts don't add up. “20% off, plus an extra 10% off” is 0.8 × 0.9 = 0.72, so 28% off in total, not 30%.