Decimal to Fraction Calculator
Convert decimal numbers to fractions in simplest form. Perfect for understanding fractions, exact representations, and mathematical conversions.
Convert Decimal to Fraction
Enter a decimal number to convert it to fraction form:
For 0.5: Multiply by 10ยน = 5, so 5/10 = 1/2
For 0.25: Multiply by 10ยฒ = 25, so 25/100 = 1/4
Understanding Decimal to Fraction Conversion
Converting decimals to fractions is essential for understanding the relationship between these two number representations. Every terminating decimal can be expressed as an exact fraction, and repeating decimals can be expressed as fractions with repeating patterns in the denominator.
The Conversion Process
๐ข Terminating Decimals
Count decimal places (n)
Multiply by 10^n to get integer
Use 10^n as denominator
Simplify the fraction
๐ Repeating Decimals
Identify repeating pattern
Create equation with variable
Solve for the variable
Express as fraction
๐ฏ Fraction Simplification
Find GCD of numerator and denominator
Divide both by the GCD
Result is simplest form
Always check for further simplification
๐ก Pro Tip: Not all decimals can be expressed as exact fractions. Irrational numbers like ฯ (3.14159...) or โ2 (1.41421...) have infinite non-repeating decimal expansions and cannot be converted to exact fractions.
Common Decimal to Fraction Conversions
| Decimal | Fraction | Simplified | Description |
|---|---|---|---|
| 0.5 | 5/10 | 1/2 | One half |
| 0.25 | 25/100 | 1/4 | One quarter |
| 0.75 | 75/100 | 3/4 | Three quarters |
| 0.2 | 2/10 | 1/5 | One fifth |
| 0.125 | 125/1000 | 1/8 | One eighth |
| 0.6 | 6/10 | 3/5 | Three fifths |
| 0.4 | 4/10 | 2/5 | Two fifths |
| 1.5 | 15/10 | 3/2 | Three halves |
| 2.25 | 225/100 | 9/4 | Nine quarters |
Step-by-Step Conversion Examples
๐ Example 1: 0.5
1. Count decimal places: 1 place
2. Multiply by 10ยน: 0.5 ร 10 = 5
3. Fraction: 5/10
4. Simplify: divide by 5 = 1/2
๐ Example 2: 0.25
1. Count decimal places: 2 places
2. Multiply by 10ยฒ: 0.25 ร 100 = 25
3. Fraction: 25/100
4. Simplify: divide by 25 = 1/4
๐ Example 3: 0.6
1. Count decimal places: 1 place
2. Multiply by 10ยน: 0.6 ร 10 = 6
3. Fraction: 6/10
4. Simplify: divide by 2 = 3/5
Rational vs Irrational Numbers
๐งฎ Rational Numbers
Can be expressed as fractions
Terminating or repeating decimals
Examples: 0.5 = 1/2, 0.333... = 1/3
Countably infinite set
๐ข Irrational Numbers
Cannot be expressed as exact fractions
Infinite non-repeating decimals
Examples: ฯ, โ2, e
Uncountably infinite set
๐ฏ Real Numbers
Include both rational and irrational
All decimals and fractions
Complete number system
Includes integers, rationals, irrationals
Practical Applications
๐ Mathematics Education
Understanding number representations
Comparing fractions and decimals
Solving fraction problems
Building mathematical reasoning
๐ฉโ๐ณ Cooking & Baking
Converting measurements to fractions
Recipe scaling calculations
Understanding ingredient ratios
Precision cooking techniques
๐๏ธ Engineering & Construction
Converting decimal dimensions
Working with architectural plans
Material cutting specifications
Precision measurement tools
๐ฐ Finance & Accounting
Converting interest rates
Working with financial ratios
Tax calculation precision
Budget planning accuracy
Repeating Decimal Conversion
| Repeating Decimal | Conversion Method | Fraction Result | Explanation |
|---|---|---|---|
| 0.333... | Let x = 0.333... 10x = 3.333... 10x - x = 3.333... - 0.333... 9x = 3 x = 3/9 = 1/3 |
1/3 | Multiply by 10, subtract original |
| 0.142857... | Let x = 0.142857... Multiply by appropriate power Solve resulting equation |
1/7 | Pattern repeats every 6 digits |
| 0.1666... | Let x = 0.1666... 10x = 1.666... 9x = 1.5 x = 1.5/9 = 1/6 |
1/6 | 6 repeats, so multiply by 10 |
Educational Benefits
๐ง Number Sense Development
Understanding different representations
Connecting fractions and decimals
Building mathematical flexibility
Developing computational fluency
๐ Pattern Recognition
Identifying terminating vs repeating
Understanding decimal expansions
Recognizing rational vs irrational
Developing mathematical insight
๐ Problem-Solving Skills
Applying conversion techniques
Choosing appropriate methods
Verifying solution accuracy
Developing systematic approaches
Common Conversion Mistakes
โ Wrong Power of 10
Always count decimal places accurately
Use correct power of 10
0.01 needs 10ยฒ, not 10ยน
Double-check place values
โ Forgetting to Simplify
Always reduce fraction to simplest terms
Find GCD of numerator and denominator
Divide both by the GCD
Check for further simplification
โ Negative Numbers
Handle signs carefully
Negative decimals give negative fractions
Sign applies to entire fraction
Don't lose the negative sign