Decimal to Fraction Calculator
Convert any decimal into a simplified fraction and mixed number, with the simplification steps shown.
Converting a decimal measurement into a usable fraction comes up constantly in woodworking, cooking, sewing, and math homework, and doing it by hand means finding a common denominator and simplifying correctly. This decimal to fraction calculator takes any decimal number and instantly returns the simplified fraction, the unsimplified version before reducing, and a mixed number when the value is greater than one. It is built for students checking their work, carpenters converting tape measure readings, and anyone who needs an exact fraction rather than a rounded decimal. A step-by-step breakdown shows exactly how the fraction was simplified, including the greatest common divisor used to reduce it. A reverse mode flips the process, converting any fraction back into its decimal equivalent. It also helps translate measurements between trades, since a contractor's tape measure reading in decimal inches often needs to be expressed as a fraction for lumber or hardware specifications. A common fractions reference table at the bottom lists frequently used conversions like 1/3, 1/8, and 1/16 for quick lookup.
Decimal Number
5/8
Unsimplified Fraction
625/1000
Simplification Steps
Common Fractions Reference
| Fraction | Decimal |
|---|---|
| 1/2 | 0.5 |
| 1/3 | 0.333... |
| 2/3 | 0.667... |
| 1/4 | 0.25 |
| 3/4 | 0.75 |
| 1/5 | 0.2 |
| 1/8 | 0.125 |
| 3/8 | 0.375 |
| 1/16 | 0.0625 |
How to Use This Calculator
1. Choose a mode
Use Decimal to Fraction or switch to Fraction to Decimal.
2. Enter your number
Type a decimal value, or a numerator and denominator in reverse mode.
3. Read the simplified and unsimplified fractions
Both forms display along with a mixed number when applicable.
4. Review the simplification steps
See exactly how the greatest common divisor was used to reduce the fraction.
How It Works
Fraction = Decimal × 10^(decimal places) ÷ 10^(decimal places), then divide by the GCDExample: 0.625 has 3 decimal places, so it becomes 625/1000. The greatest common divisor of 625 and 1000 is 125. Dividing both by 125 gives 5/8, the simplified fraction.
Frequently Asked Questions
How do I convert a decimal to a fraction?
Write the decimal as a fraction with a power of 10 as the denominator, matching the number of decimal places. Then divide the numerator and denominator by their greatest common divisor to simplify. For example, 0.625 becomes 625/1000, which simplifies to 5/8.
What is the difference between a simplified and unsimplified fraction?
An unsimplified fraction is the direct result of placing the decimal over a power of 10, such as 625/1000. A simplified fraction divides both numbers by their greatest common divisor to reach the smallest equivalent form, such as 5/8.
What is a mixed number?
A mixed number expresses a value greater than 1 as a whole number plus a fraction, such as 1 5/8 instead of 13/8. This calculator shows the mixed number whenever the decimal has a whole number part and a fractional remainder.
How do I convert a fraction to a decimal?
Divide the numerator by the denominator. Switch to Fraction to Decimal mode, enter your numerator and denominator, and the result appears instantly along with the simplified fraction.
Can this calculator handle repeating decimals?
It converts up to 12 decimal places entered directly. For known repeating fractions like 1/3, the reference table below shows the common decimal approximation.