Decimal to Fraction Converter
Convert any decimal to a fraction instantly with our online decimal to fraction converter. Get accurate, simplified results with step-by-step solutions. Perfect for students, teachers, and professionals working with math calculations.
How to Convert Decimals to Fractions?
Converting decimals to fractions is a fundamental mathematical operation. Here's how it works:
1. Identify the decimal places: Count how many digits are after the decimal point.
2. Write as a fraction: Place the decimal number (without the point) over a power of 10 (10, 100, 1000, etc.) based on the number of decimal places.
3. Simplify: Reduce the fraction to its simplest form by dividing both numerator and denominator by their greatest common divisor (GCD).
Example: 0.75 → 75/100 → 3/4 (after simplification)
Conversion Principles
1. Decimal Place Value
Each decimal place represents a power of 10. The first place after the decimal point is tenths (1/10), the second is hundredths (1/100), the third is thousandths (1/1000), and so on.
2. Creating the Initial Fraction
To convert a decimal to a fraction, count the decimal places (n), then write the number without the decimal point as the numerator and 10^n as the denominator. For example, 0.375 has 3 decimal places, so it becomes 375/1000.
3. Simplification Using GCD
After creating the initial fraction, simplify it by finding the Greatest Common Divisor (GCD) of the numerator and denominator. Divide both by the GCD to get the simplest form. For 375/1000, the GCD is 125, giving us 3/8.
4. Mixed Numbers
If the decimal is greater than 1 (like 2.5), you can express it as a mixed number. Separate the whole number part from the decimal part. Convert only the decimal part to a fraction, then combine: 2.5 = 2 + 0.5 = 2 + 1/2 = 2 1/2.
5. Repeating Decimals
- Repeating decimals (like 0.333...) require special handling
- For simple repeating decimals, use algebraic methods or known patterns
- 0.333... = 1/3, 0.666... = 2/3, 0.142857... = 1/7
- This converter uses precision settings to approximate repeating decimals
6. Accuracy Considerations
Some decimals are exact (like 0.5 = 1/2), while others are approximations. Repeating decimals cannot be perfectly represented in finite decimal form, so the converter uses the specified precision to create the best fractional approximation.
Conversion Examples
0.5 → 1/2
Simple half
0.25 → 1/4
Quarter
0.75 → 3/4
Three quarters
0.125 → 1/8
One eighth
0.2 → 1/5
One fifth
0.333 → 333/1000 ≈ 1/3
Approximate third
2.5 → 5/2 or 2 1/2
Mixed number
1.25 → 5/4 or 1 1/4
Mixed number
0.875 → 7/8
Seven eighths
3.75 → 15/4 or 3 3/4
Mixed number
Common Decimal to Fraction Conversions
0.1 = 1/10
0.2 = 1/5
0.25 = 1/4
0.3 = 3/10
0.333... = 1/3
0.4 = 2/5
0.5 = 1/2
0.6 = 3/5
0.666... = 2/3
0.7 = 7/10
0.75 = 3/4
0.8 = 4/5
0.9 = 9/10
