Decimal to Fraction Converter
Result:
Our decimal to fraction converter instantly converts any decimal number to its simplest fractional form. Whether you're working with terminating decimals, repeating decimals, or mixed numbers, our tool provides accurate results with step-by-step explanations.
Understanding Decimal to Fraction Conversion
Converting decimals to fractions is a fundamental mathematical skill that bridges the gap between different number representations. A decimal number represents parts of a whole using place values based on powers of 10, while a fraction shows the same relationship as a ratio between two integers.
Why Convert Decimals to Fractions?
- Exact Representation: Fractions provide exact values without rounding errors
- Mathematical Operations: Some calculations are easier with fractions
- Pattern Recognition: Fractions reveal mathematical relationships more clearly
- Academic Requirements: Many educational contexts require fractional answers
Step-by-Step Conversion Process
Method 1: Terminating Decimals
- Count decimal places: Determine how many digits appear after the decimal point
- Create the fraction: Use the decimal digits as numerator and appropriate power of 10 as denominator
- Simplify: Find the Greatest Common Divisor (GCD) and reduce the fraction
Example: Convert 0.375 to a fraction
Step 1: 0.375 has 3 decimal places
Step 2: 375/1000 (375 over 1000)
Step 3: GCD(375, 1000) = 125
Step 4: 375 ÷ 125 = 3, 1000 ÷ 125 = 8
Result: 0.375 = 3/8
Method 2: Repeating Decimals
For repeating decimals like 0.333... or 0.142857142857..., use algebraic methods:
- Let x = the repeating decimal
- Multiply by appropriate power of 10 to align repeating blocks
- Subtract original equation
- Solve for x and simplify
Example: Convert 0.333... to a fraction
Let x = 0.333...
10x = 3.333...
10x - x = 3.333... - 0.333...
9x = 3
x = 3/9 = 1/3
Result: 0.333... = 1/3
Common Decimal-Fraction Conversions
Memorizing these common conversions can speed up your mathematical work:
Simple Fractions
| Decimal | Fraction |
|---|---|
| 0.5 | 1/2 |
| 0.25 | 1/4 |
| 0.75 | 3/4 |
| 0.2 | 1/5 |
| 0.4 | 2/5 |
| 0.6 | 3/5 |
| 0.8 | 4/5 |
Eighths & Thirds
| Decimal | Fraction |
|---|---|
| 0.125 | 1/8 |
| 0.375 | 3/8 |
| 0.625 | 5/8 |
| 0.875 | 7/8 |
| 0.333... | 1/3 |
| 0.666... | 2/3 |
| 0.1666... | 1/6 |
Other Common Fractions
| Decimal | Fraction |
|---|---|
| 0.1 | 1/10 |
| 0.3 | 3/10 |
| 0.7 | 7/10 |
| 0.9 | 9/10 |
| 0.0625 | 1/16 |
| 0.1875 | 3/16 |
| 0.3125 | 5/16 |
Practical Applications
In Cooking & Baking
Recipe measurements often require precise fractional amounts. Converting 0.25 cups to 1/4 cup or 0.375 teaspoons to 3/8 teaspoon ensures accuracy in your culinary creations.
In Construction & Engineering
Building plans and technical drawings frequently use fractional measurements. Converting 0.75 inches to 3/4 inch helps ensure proper fitting and assembly.
In Finance & Investing
Stock prices and financial calculations often benefit from fractional representation. Understanding that 0.125 equals 1/8 can help in analyzing price movements and calculations.
In Academic Settings
Mathematics, physics, and chemistry courses frequently require students to express answers as simplified fractions rather than decimals for exact representation.
Tips for Success
Pro Tips
- Double-check your work: Convert your final fraction back to decimal to verify accuracy
- Always simplify: Reduce fractions to their lowest terms by finding the GCD
- Recognize patterns: Many decimals have predictable fractional equivalents
- Practice mental math: Learn common conversions to speed up calculations
Frequently Asked Questions
0.75 has 2 decimal places, so write it as 75/100. Find GCD(75,100) = 25. Divide: 75÷25 = 3, 100÷25 = 4. Therefore, 0.75 = 3/4.
For 1.25: The whole number part is 1. Convert 0.25 to 1/4. Result: 1.25 = 1¼ (one and one-quarter) or improper fraction 5/4.
Yes! All terminating and repeating decimals can be expressed as fractions. Non-repeating, infinite decimals (like π) can only be approximated as fractions.
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