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Percentage — Definition, Formula & Examples

Percentage is a way of expressing a number as a part out of 100. For example, 25% means 25 out of every 100, which is the same as the fraction 25100\frac{25}{100} or the decimal 0.25.

A percentage is a dimensionless ratio multiplied by 100 and denoted with the symbol %. If a quantity aa is some part of a whole bb, then the percentage is given by ab×100%\frac{a}{b} \times 100\%. Percentages provide a standardized scale (0–100 for parts within a whole, though values above 100% and below 0% are valid) for comparing proportions.

Key Formula

Percentage=PartWhole×100\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100
Where:
  • Part\text{Part} = The portion of the whole you are measuring
  • Whole\text{Whole} = The total or reference amount

How It Works

You use percentages whenever you want to describe how large one quantity is relative to another on a uniform scale of 100. To find a percentage of a number, convert the percent to a decimal and multiply: for instance, 20% of 50 is 0.20×50=100.20 \times 50 = 10. To convert a fraction to a percentage, divide the numerator by the denominator and multiply by 100. Going the other direction, divide a percentage by 100 to get its decimal form, or write it over 100 and simplify to get its fraction form.

Worked Example

Problem: You scored 36 out of 45 on a test. What is your score as a percentage?
Step 1: Write the fraction of correct answers.
3645\frac{36}{45}
Step 2: Divide the numerator by the denominator.
36÷45=0.836 \div 45 = 0.8
Step 3: Multiply by 100 to convert to a percentage.
0.8×100=80%0.8 \times 100 = 80\%
Answer: Your test score is 80%.

Another Example

Problem: A jacket originally costs $60. It is on sale for 15% off. What is the sale price?
Step 1: Convert 15% to a decimal.
15%=0.1515\% = 0.15
Step 2: Multiply the original price by the decimal to find the discount amount.
0.15×60=90.15 \times 60 = 9
Step 3: Subtract the discount from the original price.
60−9=5160 - 9 = 51
Answer: The sale price is $51.

Visualization

Why It Matters

Percentages appear constantly in everyday life — sales tax, tips, interest rates, exam grades, and statistics all rely on them. In middle-school math courses, mastering percentages is essential before tackling topics like proportional reasoning, probability, and data analysis. Careers in finance, healthcare, retail, and science use percentage calculations daily to interpret data and make decisions.

Common Mistakes

Mistake: Forgetting to divide by 100 when converting a percentage to a decimal (e.g., using 25 instead of 0.25).
Correction: Always move the decimal point two places to the left: 25%=0.2525\% = 0.25, not 25.
Mistake: Confusing "percent of" with "percent increase." For example, treating 30% of 200 the same as a 30% increase on 200.
Correction: 30% of 200 is 0.30×200=600.30 \times 200 = 60. A 30% increase on 200 means 200+60=260200 + 60 = 260. The operations are different.

Related Terms

  • Decimal — Percentages convert directly to decimals
  • Fraction — A percentage is a fraction with denominator 100
  • Ratio — Percentages express ratios on a scale of 100
  • Numerator — The percentage value acts as the numerator over 100
  • Denominator — 100 is the implied denominator in any percentage
  • Proper Fraction — Percentages under 100% correspond to proper fractions
  • Fraction Rules — Simplifying percentage fractions uses fraction rules