Percent / Percentage
A percent is a number expressed as a fraction of 100, using the symbol %. For example, 25% means 25 out of 100, which is the same as the fraction or the decimal 0.25.
A percentage is a dimensionless ratio that represents a proportion relative to 100. If a quantity is some part of a whole , the percentage is calculated as . The word comes from the Latin *per centum*, meaning "by the hundred." Percentages provide a standardized way to compare ratios that may have different denominators.
Key Formula
Where:
- = the portion of the whole you are measuring
- = the total or reference amount
Worked Example
Problem: A student scored 36 out of 50 on a test. What is their score as a percentage?
Step 1: Identify the part and the whole. The part is 36 (points earned) and the whole is 50 (total points).
Step 2: Divide the part by the whole.
Step 3: Multiply by 100 to convert to a percentage.
Step 4: Attach the percent symbol.
Answer: The student scored 72% on the test.
Visualization
Why It Matters
Percentages appear everywhere in daily life — sales tax, discounts, interest rates, exam scores, and statistics. Because they always use 100 as the reference point, percentages make it easy to compare quantities that originally had different totals. Understanding percentages is essential for financial literacy, interpreting data, and working with probability.
Common Mistakes
Mistake: Dividing the whole by the part instead of the part by the whole.
Correction: Always place the part (the smaller or measured quantity) in the numerator and the whole (the total) in the denominator: .
Mistake: Forgetting to multiply by 100 when converting a decimal to a percent (e.g., writing 0.36 instead of 36%).
Correction: A decimal like 0.36 must be multiplied by 100 to become a percentage. Conversely, to go from a percent to a decimal, divide by 100.