Most percentage errors come from choosing the wrong reference value rather than from difficult arithmetic. Naming the part, whole, old value, and new value prevents many mistakes.
Reversing the part and the whole
To find what percentage 30 is of 120, calculate 30 ÷ 120, not 120 ÷ 30. Ask: “Thirty is part of what total?” The answer is 25%, not 400%.
Adding stacked discounts
A 20% discount followed by another 10% discount is not 30% off. You pay 80% and then 90% of the reduced price: 0.8 × 0.9 = 0.72, so the total discount is 28%.
Confusing percent with percentage points
A rate rising from 5% to 7% increases by two percentage points but by 40% relative to the original rate. Use the correct phrase to avoid exaggerating or understating the change.
Rounding too early
Keep extra decimal places during the calculation and round only the final answer. Early rounding can create noticeable errors when several percentages are combined.
A calculator is often the quickest way to check your mental math. The important part is using the right starting value.
Open a calculator →Common questions
Should I divide by the old or new value?
For percentage change, divide by the old or starting value.
Can I add two consecutive percentage changes?
Only as a rough estimate. For an exact result, multiply the change factors.
How many decimal places should I use?
Use enough for the decision. Money commonly uses two decimals; reporting rates may need one or two.
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