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
Worked Example: Converting 0.625
The decimal 0.625 has three decimal places, so write it as 625/1000. The greatest common divisor of 625 and 1000 is 125. Dividing both by 125 gives 5/8 — a common measurement in woodworking and hardware sizing. The converter performs this GCD simplification automatically and also shows mixed numbers for values greater than 1.
Frequently Asked Questions
How do I convert a decimal like 0.375 to a fraction?+
Enter 0.375 and the converter writes it as 375/1000, then divides numerator and denominator by their greatest common divisor (125) to get 3/8. Every result is shown fully simplified, and decimals greater than 1 are also displayed as mixed numbers, such as 2.5 becoming 5/2 or 2 1/2.
Can it convert fractions back to decimals?+
Yes. Switch to the Fraction to Decimal tab, enter a numerator and denominator, and the tool divides them for you. This makes it easy to check work in both directions, for example confirming that 3/8 equals 0.375.
How does it handle repeating decimals like 0.333?+
A truncated repeating decimal converts to the closest terminating fraction, so 0.333 gives 333/1000 rather than exactly 1/3. Entering more repeating digits and raising the precision setting gets the result closer to the true fraction — 0.333333 simplifies to a fraction nearly identical to 1/3.
What is a mixed number and when is it shown?+
A mixed number combines a whole number with a proper fraction, such as 2 1/2 instead of 5/2. Whenever the decimal you enter is greater than 1 (or less than -1), the converter shows both the improper fraction and the equivalent mixed number, which is the format most often used in cooking and carpentry.
Is this decimal to fraction converter free and mobile-friendly?+
Yes. It is completely free with no sign-up, and all conversion happens instantly in your browser — nothing is uploaded to a server. It works on any device, including phones and tablets.
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