Percent means "per hundred" (just as there are 100 cents in a dollar). A percent is a ratio whose second number is 100, so you can read it in hundredths, the place you met in decimals.
Key idea
$35\%$ means 35 out of every 100: $35\% = \frac{35}{100} = 0.35$.
Why it works
Because the whole is cut into 100 equal parts, a percent counts hundredths. That is why 35% is the same number as $\frac{35}{100}$ and as 0.35 (35 hundredths). To write a part out of some other whole as a percent, make an equivalent ratio with 100 as the whole.
Worked example: Out of 20
7 of the 20 questions on a quiz were about fractions. What percent is that?
- Make the whole 100: $20 \times 5 = 100$.
- Multiply the part by 5 too: $7 \times 5 = 35$.
- $7 : 20 = 35 : 100$.
Answer: 35%.
Worked example: A tiny percent
Write $0.5\%$ as a decimal.
- $0.5\%$ means 0.5 per 100: $0.5 \div 100$.
- Dividing by 100 moves each digit two places to the right: $0.005$.
- That is half of one hundredth.
Answer: $0.005$
| Percent | Fraction | Decimal |
|---|---|---|
| $50\%$ | $\frac{1}{2}$ | $0.5$ |
| $25\%$ | $\frac{1}{4}$ | $0.25$ |
| $10\%$ | $\frac{1}{10}$ | $0.1$ |
| $1\%$ | $\frac{1}{100}$ | $0.01$ |
| $0.5\%$ | $\frac{1}{200}$ | $0.005$ |
| $150\%$ | $\frac{3}{2}$ | $1.5$ |
Common mistake
$0.5\%$ is not $50\%$. Fifty percent is half of the whole; half a percent is half of one hundredth, which is 1 part in 200. Quick check: write both as decimals. $50\% = 0.50$ but $0.5\% = 0.005$, a hundred times smaller. On the grid, 50% fills half the squares; 0.5% would fill half of a single square.