What a percentage means
A percentage expresses a quantity per hundred. Fifty percent means 50 out of 100, which is the same as one half. Twenty percent means 20 out of 100, or 0.20 in decimal form.
To find a percentage of a number, convert the percentage to a decimal and multiply. For example, 15% of 200 is 0.15 × 200 = 30.
Percentage change is a comparison
Percentage change compares the difference between a new value and an original value with the original value. The denominator matters: a move from 80 to 100 is a 25% increase because the 20-point increase is one quarter of the original 80.
A decrease uses the same relationship. Moving from 100 to 80 is a 20% decrease, not 25%, because the original value in that direction is 100.
Discounts and percent off
A discount removes a percentage of the original price. A 25% discount on $120 saves $30 and leaves a sale price of $90.
For multiple discounts, applying the percentages separately is usually more accurate than simply adding them. For example, 20% off followed by another 10% off leaves 72% of the original price, which is a total reduction of 28%.
Common mistakes to avoid
The most common mistakes are using the wrong base value, mixing percentage points with percentage change, and rounding too early. Keep the full value during the calculation and round the displayed result at the end.
- Use the original value as the base for percentage change.
- Convert percent to decimal by dividing by 100.
- Distinguish a 5 percentage-point change from a 5% relative change.
- Keep units consistent before comparing values.