1. Treating percentage points as percent change
If an interest rate moves from 4% to 5%, it increased by one percentage point. Relative to the original 4%, however, the increase is 25%. Both statements can be correct, but they answer different questions. Use “percentage points” when subtracting two rates directly.
2. Assuming equal increases and decreases cancel
A 20% increase followed by a 20% decrease does not return to the starting value. Starting at 100, the increase creates 120. Reducing 120 by 20% removes 24, leaving 96. The second percentage acts on a different base.
3. Adding consecutive discounts
A 20% discount followed by another 10% discount is not usually a 30% discount. A price of 100 falls to 80, then 10% of 80 removes another 8. The final price is 72, equivalent to a 28% total discount.
4. Reversing a percentage with subtraction
If a final price of 115 includes 15% tax, subtracting 15% of 115 does not recover the net price. Divide by 1.15 instead. Reversing growth, tax or markup usually requires division because the final amount has a different base.
5. Ignoring the reference group
“30% higher” is incomplete without the comparison. Higher than last year, higher than a competitor or higher than a forecast can produce very different interpretations. Before calculating, write the original or reference value in plain language.
A good percentage check includes three labels: original value, new or partial value, and the question being asked. Clear labels prevent more mistakes than additional decimal places.