Decimal to Fraction Calculator
Convert decimal numbers to fractions in simplest form. Perfect for educational purposes and finding exact rational representations of decimals.
Convert Decimal to Fraction
Enter a decimal number to convert to a fraction:
Example: 0.75 = 3/4, 0.333... = 1/3
Decimal to Fraction Conversion
Converting decimals to fractions is an important mathematical skill that helps us understand the relationship between decimals and rational numbers. Every terminating decimal can be converted to a fraction, and many repeating decimals can also be expressed as fractions.
How Decimal to Fraction Conversion Works
📊 Terminating Decimals
Decimals that end (like 0.5, 0.75, 0.125)
🔄 Repeating Decimals
Decimals that repeat (like 0.333..., 0.142857...)
📐 Fraction Simplification
Reducing fractions to their lowest terms
🎯 Exact Representation
Fractions provide exact rational values
Conversion Method
| Step | Example: 0.75 | Formula |
|---|---|---|
| 1. Count decimal places | 0.75 has 2 decimal places | n = 2 |
| 2. Multiply by 10^n | 0.75 × 100 = 75 | decimal × 10^n = numerator |
| 3. Set denominator | Denominator = 100 | 10^n = denominator |
| 4. Simplify fraction | 75/100 = 3/4 | ÷ GCD(75,100) = 25 |
Common Decimal Conversions
| Decimal | Fraction | Simplified | Calculation |
|---|---|---|---|
| 0.5 | 5/10 | 1/2 | 5÷5/10÷5 = 1/2 |
| 0.25 | 25/100 | 1/4 | 25÷25/100÷25 = 1/4 |
| 0.75 | 75/100 | 3/4 | 75÷25/100÷25 = 3/4 |
| 0.125 | 125/1000 | 1/8 | 125÷125/1000÷125 = 1/8 |
| 0.2 | 2/10 | 1/5 | 2÷2/10÷2 = 1/5 |
| 0.4 | 4/10 | 2/5 | 4÷2/10÷2 = 2/5 |
💡 Pro Tip: To convert a decimal to a fraction, count the decimal places (n), multiply by 10^n to get the numerator, use 10^n as the denominator, then simplify by dividing by the GCD.
Repeating Decimals
For repeating decimals, the method is more complex but follows the same principle:
| Repeating Decimal | Fraction | Method |
|---|---|---|
| 0.333... | 1/3 | Let x = 0.333..., then 10x = 3.333..., so 10x - x = 3.333... - 0.333... = 3, therefore 9x = 3, x = 1/3 |
| 0.142857... | 1/7 | Let x = 0.142857..., then 1000000x = 142857.142857..., so 999999x = 142857, x = 142857/999999 = 1/7 |
| 0.666... | 2/3 | Let x = 0.666..., then 10x = 6.666..., so 10x - x = 6.666... - 0.666... = 6, therefore 9x = 6, x = 2/3 |
Educational Applications
📚 Mathematics Education
Understanding the relationship between decimals and fractions
🔬 Science & Engineering
Converting measurements and calculations to exact values
💰 Finance & Accounting
Converting decimal interest rates to fractional form
🏗️ Construction & Carpentry
Converting decimal measurements to fractions for precision
Practical Examples
| Context | Decimal | Fraction | Use Case |
|---|---|---|---|
| Cooking | 0.5 | 1/2 | Half cup of flour |
| Cooking | 0.75 | 3/4 | Three-quarters cup of sugar |
| Cooking | 0.25 | 1/4 | Quarter teaspoon of salt |
| Construction | 0.125 | 1/8 | One-eighth inch measurement |
| Finance | 0.05 | 1/20 | 5% interest rate |
| Finance | 0.025 | 1/40 | 2.5% service charge |
Why Convert Decimals to Fractions?
- Exact Representation: Fractions provide exact values while decimals may be approximations
- Mathematical Operations: Easier to add, subtract, multiply, and divide fractions
- Measurement Precision: Some contexts require exact fractional measurements
- Educational Value: Understanding the relationship between different number representations
- Pattern Recognition: Helps identify mathematical patterns and relationships
Common Decimal to Fraction Patterns
🔢 Halves & Quarters
0.5 = 1/2, 0.25 = 1/4, 0.75 = 3/4
📐 Eighths & Sixteenths
0.125 = 1/8, 0.0625 = 1/16, 0.1875 = 3/16
💰 Common Percentages
0.2 = 1/5 (20%), 0.25 = 1/4 (25%), 0.4 = 2/5 (40%)
⚗️ Scientific Measurements
0.001 = 1/1000, 0.01 = 1/100, 0.1 = 1/10