Percent Sign — Definition, Formula & Examples

The percent sign (%) is the symbol placed after a number to show that it represents a part out of 100. For example, 25% means 25 out of 100.

The symbol %, read as "percent," denotes that the preceding numeral expresses a ratio with a denominator of 100. Writing $n\%$ is equivalent to writing $\frac{n}{100}$ or $n \times 0.01$ .

Key Formula

n\% = \frac{n}{100}

Where:

$n$ = The number written before the percent sign

How It Works

You write the percent sign directly after a number with no space, like 50%. To convert a percent to a decimal, remove the % sign and divide by 100. To convert a percent to a fraction, place the number over 100 and simplify. The word "percent" itself comes from the Latin "per centum," meaning "by the hundred."

Worked Example

Problem: Write 40% as a fraction and as a decimal.

As a fraction: Place 40 over 100.

40\% = \frac{40}{100}

Simplify: Divide the numerator and denominator by 20.

\frac{40}{100} = \frac{2}{5}

As a decimal: Divide 40 by 100 by moving the decimal point two places to the left.

40\% = 0.40

Answer: 40% equals

\frac{2}{5}

0.4

Why It Matters

You encounter the percent sign in store discounts, test scores, weather forecasts, and nutrition labels. Understanding what % means is essential for comparing quantities in everyday life and in math courses from elementary school through statistics.

Common Mistakes

Mistake: Confusing 5% with 0.5 instead of 0.05.

Correction: To convert a percent to a decimal, divide by 100 (move the decimal two places left). So 5% = 0.05, not 0.5.