Decimal ↔ Fraction Converter
Higher precision gives more accurate fractions but larger denominators
Common Fractions Reference
How It Works
Decimal to Fraction: The converter multiplies the decimal by a power of 10 to eliminate the decimal point, then simplifies using the Greatest Common Divisor (GCD).
Example: 0.75 → 75/100 → simplified to 3/4
Repeating Decimals: For repeating decimals like 0.333..., increase the precision slider for more accurate fractions.
Understanding Decimal to Fraction Conversion
Converting decimals to fractions is a fundamental math skill used in cooking, construction, engineering, and everyday life. This converter helps you quickly transform any decimal number into its fractional equivalent.
How to Convert Decimals to Fractions
The process involves these steps:
- Count decimal places: Determine how many digits are after the decimal point.
- Create the fraction: Write the decimal digits as the numerator over a denominator of 1 followed by zeros equal to the decimal places.
- Simplify: Divide both numerator and denominator by their Greatest Common Divisor (GCD).
Examples
| Decimal | Initial Fraction | Simplified | Mixed Number |
|---|---|---|---|
| 0.5 | 5/10 | 1/2 | - |
| 0.75 | 75/100 | 3/4 | - |
| 0.125 | 125/1000 | 1/8 | - |
| 2.5 | 25/10 | 5/2 | 2 1/2 |
| 3.25 | 325/100 | 13/4 | 3 1/4 |
Repeating Decimals
Some fractions produce repeating decimals when converted. For example:
- 1/3 = 0.333... (repeating)
- 1/6 = 0.1666... (repeating)
- 1/7 = 0.142857... (repeating pattern)
When converting these back to fractions, increasing the precision setting will help get closer to the exact fraction.
Common Uses
- Cooking: Converting metric measurements to imperial fractions
- Construction: Working with fractional inch measurements
- Finance: Understanding stock prices in fractional format
- Education: Learning fraction-decimal relationships
- Music: Understanding time signatures and note values