Decimal to Fraction Converter
Enter a terminating decimal (like 0.125, -2.75, or 3) and get the exact simplified fraction instantly.
What is a terminating decimal?
A terminating decimal is a decimal number that ends after a finite number of digits. For example, 0.5, 1.25, and 7.125 are all terminating decimals. In contrast, values like 0.333... continue forever and are called repeating decimals.
Every terminating decimal can be written as a fraction with a denominator of a power of 10 (10, 100, 1000, and so on), then simplified to lowest terms. That is exactly what this calculator automates.
How this terminating decimal to fraction calculator works
Step 1: Count digits after the decimal point
If your number has n digits after the decimal, set the denominator to 10n.
Step 2: Remove the decimal point for the numerator
Write all digits as a whole number. That becomes the numerator before simplification.
Step 3: Simplify using the greatest common divisor
Divide both numerator and denominator by their greatest common divisor (GCD) to get the reduced fraction.
Quick conversion examples
| Decimal | Unsimplified Fraction | Simplified Fraction |
|---|---|---|
| 0.5 | 5/10 | 1/2 |
| 2.75 | 275/100 | 11/4 |
| -0.04 | -4/100 | -1/25 |
| 3.125 | 3125/1000 | 25/8 |
Why convert decimals to fractions?
- Exact values: Fractions avoid rounding errors in algebra and finance.
- Easier comparison: You can compare ratios clearly, especially in measurements and probability.
- Math class and tests: Many teachers require answers in simplified fractional form.
- Engineering and recipes: Fractional forms are common in practical applications.
Common mistakes to avoid
- Forgetting to simplify the fraction after conversion.
- Using the wrong denominator (for example, using 100 for 0.5 instead of 10).
- Dropping the negative sign when converting a negative decimal.
- Confusing repeating decimals with terminating decimals.
FAQ
Does this tool support negative decimals?
Yes. A value like -1.2 converts to -6/5.
Can I enter whole numbers?
Yes. A whole number like 7 is already a fraction: 7/1.
Does this work for repeating decimals?
This calculator is designed for terminating decimals. Repeating decimals need a different method.