Decimal to Fraction Calculator
Convert between decimals and fractions with simplification
How to Use
- Select your input type (decimal or fraction)
- Enter the decimal number or fraction (numerator and denominator)
- Click calculate to see the conversion
- View both formats with automatic fraction simplification
Understanding Fractions and Decimals
Fractions and decimals are two different ways to represent numbers that are not whole. A fraction shows a part of a whole as a ratio (like 3/4), while a decimal uses a decimal point to show the same value (like 0.75).
Converting between these formats is essential in many fields including mathematics, science, cooking, construction, and finance. Understanding both representations helps in choosing the most appropriate format for different situations.
Conversion Methods
To convert a fraction to decimal, divide the numerator by the denominator. For example, 3/4 = 3 ÷ 4 = 0.75.
To convert a decimal to fraction, count the decimal places and use them as the denominator's power of 10. For example, 0.75 has 2 decimal places, so it becomes 75/100, which simplifies to 3/4.
Common Decimal to Fraction Conversions
| Decimal | Fraction | Simplified |
|---|---|---|
| 0.5 | 5/10 | 1/2 |
| 0.25 | 25/100 | 1/4 |
| 0.75 | 75/100 | 3/4 |
| 0.333... | 333/1000 | 1/3 |
| 0.125 | 125/1000 | 1/8 |
| 0.666... | 666/1000 | 2/3 |
Simplifying Fractions
Simplifying fractions means reducing them to their lowest terms by dividing both numerator and denominator by their Greatest Common Divisor (GCD). For example, 6/8 simplifies to 3/4 because both can be divided by 2.
A simplified fraction is easier to understand and work with. Our calculator automatically simplifies all fractions to their lowest terms.
Practical Applications
- Cooking: Converting recipe measurements between fractions and decimals
- Construction: Working with measurements in both imperial and metric systems
- Finance: Converting percentages and interest rates
- Education: Solving math problems and understanding number relationships
- Engineering: Precision calculations requiring exact fractional values
- Science: Expressing ratios and proportions in experiments
Frequently Asked Questions
- How do I convert 0.75 to a fraction?
- 0.75 has 2 decimal places, so write it as 75/100. Then simplify by dividing both numbers by their GCD (25), giving you 3/4. This calculator does this automatically.
- What is 1/3 as a decimal?
- 1/3 as a decimal is 0.333... (repeating). The decimal representation is infinite because 3 doesn't divide evenly into 1. Most calculators show it as approximately 0.333333.
- Why do some decimals convert to complex fractions?
- Some decimals, especially those with many decimal places or repeating patterns, may convert to fractions with large numerators and denominators. Simplification helps reduce these to more manageable forms.
- Can I convert improper fractions to decimals?
- Yes! Improper fractions (where the numerator is larger than the denominator, like 5/4) can be converted to decimals. 5/4 = 1.25. Our calculator handles both proper and improper fractions.