Decimal to Fraction Converter
Convert any decimal number to a simplified fraction — enter your decimal below.
How to Convert a Terminating Decimal to a Fraction
For decimals that end (terminate), follow these steps:
- Count the number of decimal places (digits after the decimal point).
- Write the digits (without the decimal point) as the numerator.
- Write 10 raised to that number of decimal places as the denominator.
- Simplify by dividing both by their GCD.
Example: Convert 0.625
- 3 decimal places → denominator is 1000
- 0.625 = 625/1000
- GCD(625, 1000) = 125
- 625/1000 = 5/8
How to Convert a Repeating Decimal to a Fraction
Use the algebraic subtraction method:
Example: Convert 0.272727... (0.27̄)
- Let x = 0.272727...
- Since 2 digits repeat, multiply by 100: 100x = 27.272727...
- Subtract: 100x - x = 27 → 99x = 27
- x = 27/99 = 3/11
Quick Reference Table
| Decimal | Fraction | Decimal | Fraction |
|---|---|---|---|
| 0.1 | 1/10 | 0.5 | 1/2 |
| 0.125 | 1/8 | 0.6 | 3/5 |
| 0.2 | 1/5 | 0.625 | 5/8 |
| 0.25 | 1/4 | 0.75 | 3/4 |
| 0.333... | 1/3 | 0.875 | 7/8 |
Real-World Applications
- Engineering: Converting 0.375" to 3/8" for fractional drill bit sizes.
- Cooking: A recipe calling for 0.25 cups is more readable as 1/4 cup.
- Finance: Interest rates and probabilities expressed as fractions for exact calculations.
- Education: Understanding the relationship between decimal and fractional representations.
Frequently Asked Questions
How do you convert a terminating decimal to a fraction?
Write the digits over a power of 10 matching the decimal places, then simplify. 0.375 = 375/1000 = 3/8 (dividing by GCD = 125).
How do you convert a repeating decimal to a fraction?
Let x equal the decimal, multiply by 10^(repeating digits), subtract to eliminate the repeat, then solve for x. For 0.333...: 10x = 3.333..., subtract x: 9x = 3, so x = 1/3.
What is 0.5 as a fraction?
0.5 = 5/10 = 1/2. One decimal place gives denominator 10; simplify by dividing numerator and denominator by GCD(5,10) = 5.
Can every decimal be written as a fraction?
Every terminating and repeating decimal is a rational number and can be written as a fraction. Irrational numbers like π = 3.14159... cannot be expressed as fractions.
Is the Decimal to Fraction converter free?
Yes, completely free. No registration, no limits, no hidden fees.