Three ways to write the same thing
Fractions, decimals and percentages are three notations for the same concept: a part relative to a whole. One-half can be written as 1/2, 0.5 or 50%. Each form is useful in different situations. Mastering the conversions between them is a core math skill.
This guide covers all six conversion directions with formulas and worked examples.
1. Fraction to decimal
Decimal = Numerator / Denominator
Divide the top number by the bottom number.
Examples:
- 3/4 = 3 / 4 = 0.75
- 1/3 = 1 / 3 = 0.333... (repeating decimal)
- 5/2 = 5 / 2 = 2.5
2. Decimal to fraction
Write the decimal over a power of 10 based on the number of decimal places, then simplify.
Steps:
- Count the decimal places.
- Write the digits (without the decimal point) over 10, 100, 1000, etc.
- Simplify by dividing numerator and denominator by their greatest common divisor.
Examples:
- 0.75 = 75/100, divide both by 25 = 3/4
- 0.2 = 2/10 = 1/5
- 0.125 = 125/1000, divide both by 125 = 1/8
- 1.5 = 15/10 = 3/2 (an improper fraction)
3. Fraction to percentage
Percentage = (Numerator / Denominator) x 100
Divide the numerator by the denominator, then multiply by 100 and add the percent sign.
Examples:
- 3/4 = (3 / 4) x 100 = 0.75 x 100 = 75%
- 1/3 = (1 / 3) x 100 = 0.333... x 100 ≈ 33.33%
- 2/5 = (2 / 5) x 100 = 0.40 x 100 = 40%
- 7/8 = (7 / 8) x 100 = 0.875 x 100 = 87.5%
Use the fraction to percentage converter for instant results.
4. Percentage to fraction
Fraction = Percentage / 100 (then simplify)
Write the percentage over 100 and reduce to the simplest form.
Examples:
- 75% = 75/100 = 3/4
- 20% = 20/100 = 1/5
- 12.5% = 12.5/100 = 125/1000 = 1/8
- 150% = 150/100 = 3/2
5. Decimal to percentage
Percentage = Decimal x 100
Multiply the decimal by 100 and add the percent sign. This is the simplest conversion of all six.
Examples:
- 0.25 x 100 = 25%
- 0.05 x 100 = 5%
- 1.2 x 100 = 120%
- 0.003 x 100 = 0.3%
Try the decimal to percentage converter to verify your conversions.
6. Percentage to decimal
Decimal = Percentage / 100
Divide the percentage by 100. This is equivalent to moving the decimal point two places to the left.
Examples:
- 25% = 25 / 100 = 0.25
- 5% = 5 / 100 = 0.05
- 120% = 120 / 100 = 1.2
- 0.3% = 0.3 / 100 = 0.003
Use the percentage to decimal converter for quick results.
Common fraction-to-percentage reference table
Memorizing these common conversions saves time on everyday calculations.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/1 | 1.0 | 100% |
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 2/3 | 0.666... | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/6 | 0.1666... | 16.67% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
| 1/25 | 0.04 | 4% |
| 1/100 | 0.01 | 1% |
The big picture
All conversions follow a simple pattern:
- To decimal: divide (fraction: numerator / denominator; percentage: / 100)
- From decimal: multiply by the target denominator (percentage: x 100; fraction: write over power of 10)
- Between fraction and percentage: go through decimal as the intermediate step
The decimal form is the universal bridge. Whenever you are stuck between a fraction and a percentage, convert to decimal first, then to the target form.
Related calculators
Convert between all three forms with dedicated tools.