Converting between fractions, decimals, and percentages is a core skill that comes up constantly — in recipes, discounts, test scores, financial returns, and statistics. The conversions follow a small set of rules that, once understood, make the process automatic.
The Key Relationship
All three formats represent the same thing — a part of a whole — just written differently:
| Fraction | Decimal | Percentage | |----------|---------|------------| | 1/2 | 0.5 | 50% | | 1/4 | 0.25 | 25% | | 3/4 | 0.75 | 75% | | 1/5 | 0.2 | 20% | | 1/3 | 0.333... | 33.33...% |
Fraction to Percentage
Method 1 — via decimal: Divide the numerator by the denominator, then multiply by 100.
Percentage = (numerator / denominator) × 100
Example: Convert 3/8 to a percentage.
3 ÷ 8 = 0.375
0.375 × 100 = 37.5%
Method 2 — scale the denominator to 100: If you can convert the denominator to 100 by multiplying by a whole number, multiply numerator and denominator by the same number.
3/4 → multiply both by 25 → 75/100 = 75%
7/20 → multiply both by 5 → 35/100 = 35%
This only works cleanly when 100 is divisible by the denominator (denominators 2, 4, 5, 10, 20, 25, 50).
Percentage to Fraction
Divide the percentage by 100, then simplify.
65% = 65/100 = 13/20
37.5% = 37.5/100 = 375/1000 = 3/8
Simplifying fractions: Divide numerator and denominator by their greatest common factor (GCF).
48/60 → GCF of 48 and 60 is 12 → 48÷12 = 4, 60÷12 = 5 → 4/5
Decimal to Percentage
Multiply by 100 (move the decimal point two places right).
0.73 → 73%
0.08 → 8%
1.25 → 125%
Percentage to Decimal
Divide by 100 (move the decimal point two places left).
42% → 0.42
7% → 0.07
130% → 1.30
Fraction to Decimal
Divide numerator by denominator.
5/8 = 5 ÷ 8 = 0.625
2/3 = 2 ÷ 3 = 0.6666... = 0.6̄
Repeating decimals (like 1/3 = 0.333...) can be written with a dot or bar above the repeating digit.
Common Conversions to Memorise
| Fraction | Decimal | % | |----------|---------|---| | 1/8 | 0.125 | 12.5% | | 1/6 | 0.1667 | 16.67% | | 1/5 | 0.2 | 20% | | 1/4 | 0.25 | 25% | | 1/3 | 0.333 | 33.3% | | 3/8 | 0.375 | 37.5% | | 2/5 | 0.4 | 40% | | 1/2 | 0.5 | 50% | | 3/5 | 0.6 | 60% | | 5/8 | 0.625 | 62.5% | | 2/3 | 0.667 | 66.7% | | 3/4 | 0.75 | 75% | | 7/8 | 0.875 | 87.5% |
Worked Exam-Style Examples
A student scores 34 out of 40. What is their percentage score?
34/40 = 0.85 = 85%
A jacket costs £120. It is reduced by 35%. What is the sale price?
35% of £120 = 0.35 × 120 = £42
Sale price = £120 − £42 = £78
A recipe uses 3/4 cup of sugar. You want to make 150% of the recipe. How much sugar?
3/4 × 1.5 = 1.125 cups = 1 and 1/8 cups
Mixed numbers: 2 and 3/4 = 2 + 3/4 = 2.75 = 275%
Why This Matters in Real Life
Finance: Interest rates are percentages (e.g. 0.375% monthly = 4.5% annually = 9/200 as a fraction).
Statistics: Probabilities expressed as fractions (3/8 chance), decimals (0.375), or percentages (37.5%) — all mean the same thing.
Cooking: Scaling recipes up or down requires fraction arithmetic.
Discounts: "Buy one get one 50% off" = effective discount of 1/4 (25%) on your total.
Use our Fraction to Percentage Calculator and Percentage Calculator for any conversion instantly.