Mistake #1: Confusing Percentage Points with Percentages
This is the number one mistake in percentage calculations, and it trips up journalists, politicians, and businesspeople regularly. Percentage points and percentages are NOT the same thing.
The Problem:
Scenario: Interest rate increases from 2% to 3%
❌ WRONG: "Interest rates increased by 1%"
✓ CORRECT: "Interest rates increased by 1 percentage point" OR "Interest rates increased by 50%"
The Explanation:
Percentage point change: The simple arithmetic difference. 3% - 2% = 1 percentage point.
Percentage change: The relative change. (3% - 2%) ÷ 2% × 100 = 50% increase.
Real-world impact: If your savings account interest goes from 2% to 3%, you're earning 50% MORE interest, not 1% more. On £10,000, that's £100 extra per year (from £200 to £300), not £10.
How to avoid this: Always specify "percentage points" when talking about arithmetic differences between percentages. Use "percent" for relative changes.
Mistake #2: Thinking Increases and Decreases Cancel Out
Many people assume that a 20% increase followed by a 20% decrease brings you back to where you started. It doesn't. This asymmetry catches people off guard.
The Classic Example:
Starting value: £100
Step 1: Increase by 20%
- 20% of £100 = £20
- New value: £100 + £20 = £120
Step 2: Decrease by 20%
- 20% of £120 = £24 (NOT £20!)
- New value: £120 - £24 = £96
Result: You end up with £96, not £100. You lost £4!
Why This Happens:
The percentage increase and decrease are calculated on DIFFERENT base values. The 20% decrease is calculated on the larger £120 amount, so it removes more money than the 20% increase added.
Stock Market Example:
Your stock goes up 50% (from $100 to $150), then drops 50% (from $150 to $75). You've lost 25% of your original investment, not broken even!
How to avoid this: Always calculate each percentage change from its actual base value. Don't assume symmetric changes cancel out—they don't.
Mistake #3: Adding Percentages Instead of Compounding
When percentages stack on top of each other, you can't just add them together. Each percentage applies to the new total, not the original.
The Trap:
Scenario: Item costs £100, you have a 20% discount coupon plus 10% student discount
❌ WRONG: "That's 30% off, so I pay £70"
✓ CORRECT: "First 20% off = £80, then 10% off £80 = £72"
Step-by-Step:
Original price: £100
After 20% discount: £100 × 0.80 = £80
After 10% discount on £80: £80 × 0.90 = £72
Total discount: £100 - £72 = £28 (28%, not 30%!)
Quick formula for compound discounts: Price × (1 - discount1) × (1 - discount2)
£100 × 0.80 × 0.90 = £72
Investment Example (Works Both Ways):
Investment grows 10% per year for 3 years. You might think: "10% + 10% + 10% = 30% total growth." But actually:
Year 1: £1,000 × 1.10 = £1,100
Year 2: £1,100 × 1.10 = £1,210
Year 3: £1,210 × 1.10 = £1,331
Total growth: 33.1%, not 30%! Compounding works in your favor.
How to avoid this: Apply percentage changes sequentially, not additively. Each change applies to the current value, not the original.
Mistake #4: Getting the Base Value Wrong
Percentages always refer to a percentage "of" something. Using the wrong base value is one of the sneakiest mistakes because the calculation looks right—but the answer is wrong.
Common Scenario:
A company's workforce is 60% women and 40% men. The company wants to increase the percentage of men to 50%. What percentage increase in male employees is needed?
❌ WRONG THINKING: "40% to 50% = 10% increase"
This confuses percentage points with the actual increase needed.
✓ CORRECT:
Current: 40 men, 60 women (100 total)
Target: Men = 50% of total
If we hire only men, we need: 40 men to become 50% of new total
Math: 40 + X = 0.5 × (100 + X)
Solving: X = 20 new men needed
That's a 50% increase in male employees (20/40), not 10%!
Another Example:
Your salary increased from £40,000 to £50,000. Your friend's increased from £80,000 to £90,000. Who got a bigger raise?
In absolute terms: Your friend (£10,000 vs your £10,000—tied!)
In percentage terms: You got a 25% raise. Your friend got a 12.5% raise. You won!
The base value matters. £10,000 is a bigger percentage of £40,000 than of £80,000.
How to avoid this: Always ask "percentage of WHAT?" Make sure you're clear on the base value before calculating.
Mistake #5: Rounding Too Early in Multi-Step Calculations
Rounding is necessary, but doing it too early in a calculation can compound errors. This is especially dangerous in financial contexts where small errors multiply.
The Problem:
Calculate 17.5% of £127.46, then add it to the original
❌ WRONG WAY (rounding early):
17.5% of £127.46 = £22.30 (rounded)
Total: £127.46 + £22.30 = £149.76
✓ CORRECT WAY (keeping precision):
17.5% of £127.46 = £22.3055
Total: £127.46 + £22.3055 = £149.7655
Rounded final answer: £149.77
Difference: £0.01 (which compounds over many transactions!)
Real-World Impact:
In accounting and engineering, rounding errors can compound across thousands of calculations. This is why software keeps many decimal places internally and only rounds for display.
Famous Example:
The Patriot missile failure in 1991 was partly caused by accumulated rounding errors in time calculations. Small errors × millions of operations = disaster.
How to avoid this: Keep full precision until the final answer. Round only once, at the end. Use calculators or tools that maintain precision automatically.
Quick Reference: Avoiding Percentage Mistakes
✓ DO use "percentage points" for arithmetic differences
✓ DO remember increases and decreases don't cancel
✓ DO compound percentages, don't add them
✓ DO identify your base value first
✓ DO keep precision until the final answer
✓ DO double-check with a calculator when money is involved
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