Introduction to Percentages
Understand what the % symbol means, why percentages are useful in everyday life, and how to convert between percentages, fractions, and decimals.
What Is a Percentage?
The word percentage comes from the Latin per centum, meaning "out of one hundred". A percentage is a special way of writing a fraction with a denominator of 100. The symbol for percentage is %.
Visual: 100-Square Grid
This grid has 100 squares. The number of shaded squares equals the percentage.
35 out of 100 squares = 35% = 35/100 = 0.35
Percentages in everyday life
Benchmark Percentages
Knowing these common percentages and their fraction equivalents makes mental maths much faster.
50%
= 1/2 = 0.5
Half
25%
= 1/4 = 0.25
One quarter
10%
= 1/10 = 0.1
One tenth
20%
= 1/5 = 0.2
One fifth
Percentage Number Line
Converting Between Percentages, Fractions, and Decimals
Fraction → Percentage
Make the denominator 100, or divide and multiply by 100.
3/4 × 100 = 75%
2/5 × 100 = 40%
Decimal → Percentage
Multiply by 100 and add the % sign.
0.6 × 100 = 60%
0.45 × 100 = 45%
Percentage → Fraction
Write over 100 then simplify.
40% = 40/100 = 2/5
75% = 75/100 = 3/4
Key Vocabulary
Percentage (%)
A way of expressing a number out of 100. The symbol % means "per hundred".
Convert
To change the form of a number without changing its value — e.g. from a fraction to a percentage.
Benchmark
A well-known reference point used for estimation. E.g. 50% = 1/2 is a benchmark percentage.
Per Cent
Latin for "out of one hundred". 75 per cent = 75 out of every 100.
Worked Examples
Convert 3/5 to a percentage.
Method 1: Make denominator 100. 3/5 = 60/100 = 60%
Method 2: Divide numerator by denominator then × 100: 3 ÷ 5 = 0.6 × 100 = 60%
Answer: 3/5 = 60%
Convert 0.8 to a percentage.
Step 1: Multiply by 100: 0.8 × 100 = 80
Step 2: Add the % sign.
Answer: 0.8 = 80%
In a class of 30, 12 students have a pet. What percentage is this?
Step 1: Write as a fraction: 12/30
Step 2: Simplify: 12/30 = 2/5
Step 3: Convert to %: 2/5 = 40%
Answer: 40% of the class has a pet.
Knowledge Check
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Key Concepts Summary
- ●Percentage (%) means "out of 100".
- ●Key benchmarks: 50% = 1/2, 25% = 1/4, 10% = 1/10, 20% = 1/5.
- ●To convert a decimal to a percentage, multiply by 100.
- ●To convert a fraction to a percentage, divide the numerator by the denominator, then multiply by 100.
- ●To convert a percentage to a fraction, write it over 100, then simplify.