Percentages in everyday life: discounts, tax and marks
Percentages show up everywhere: sale tags, test scores, interest rates, nutrition labels. The word simply means "out of 100", so 35% is 35 out of every 100. Everything else is a handful of tricks for getting from a percentage to a number you care about.
The 10% shortcut
The fastest mental trick is to find 10% by moving the decimal point one place left. 10% of 64 is 6.4. From there you can build almost anything: 20% is double that, 5% is half, 15% is 10% plus 5%. For a 15% tip on $64, that is 6.40 + 3.20 = $9.60.
Percentage of an amount
Turn the percentage into a decimal (divide by 100) and multiply. 35% of 240 is 0.35 × 240 = 84.
Discounts and tax
A 25% discount means you pay 75%, so multiply the price by 0.75. A $48 item becomes $36. Sales tax goes the other way: 8% tax means you pay 108%, so multiply by 1.08. A $36 item becomes $38.88 at the till. Notice you can do both in one go: 48 × 0.75 × 1.08.
Percentage change
To measure how much something rose or fell, divide the change by the starting value. A bus fare that goes from $2.00 to $2.50 has risen by 0.50 ÷ 2.00 = 25%.
Why +50% then -50% is not break-even
Start with $100. Add 50% and you have $150. Take 50% off that and you have $75, not $100, because the second percentage is taken from a bigger number. This is why a share that falls 50% needs to rise 100% to recover. It also explains stacked discounts: 20% off followed by another 10% off is not 30% off. It is 0.8 × 0.9 = 0.72, so 28% off.
| Situation | Calculation | Result |
|---|---|---|
| 30% off $80 | 80 × 0.70 | $56.00 |
| Score 42 out of 60 | 42 ÷ 60 × 100 | 70% |
| Price up from $40 to $46 | 6 ÷ 40 × 100 | 15% increase |
| 6% tax on $25 | 25 × 1.06 | $26.50 |
Percent versus percentage points
If a savings rate moves from 4% to 5%, it has gone up by one percentage point, but in relative terms it is a 25% increase. News headlines mix the two constantly, so it is worth knowing which one you are being told.
Use the percentage calculator to check any of these, and try changing the numbers to see how the answers move.
Run your own numbers through the percentage calculator.