Percentages seem simple, but they are often counter-intuitive. Even experienced professionals, journalists, and politicians frequently make these three common errors.
1. Percentage Change vs. Percentage Points
This is the most common error in news reporting.
The Scenario
An interest rate rises from 10% to 12%.
Why? Because the actual percentage increase is 20% (since 2 is 20% of 10). When comparing two percentages, always use the term "percentage points" for the absolute difference.
2. Adding Percentages Directly
If a shop offers a "20% discount" and then an "additional 20% off", you are not getting 40% off.
The Math:
Start with $100.
First 20% off: $100 - $20 = $80.
Second 20% off: 20% of $80 is $16.
Final Price: $80 - $16 = $64.
Total savings: $36.
Actual discount: 36%, not 40%.
3. Reversing Percentages
If a stock loses 50% of its value, it needs to gain 100% to get back to where it started, not 50%.
- Start: $100
- Loss of 50%: $50
- Gain of 50% on $50: $25 (Total $75)
- Gain of 100% on $50: $50 (Total $100)
Percentages are not symmetric. The base number changes after the first operation, which changes the value of the percentage in the second operation.