How to Convert Decimal to Fraction Free — Simplified (2026)

Converting a decimal to a fraction is useful in cooking, carpentry, engineering, and mathematics — anywhere exact rational representations are clearer or required. The conversion is exact for terminating decimals (like 0.75 = 3/4) and yields a rational approximation for repeating decimals.

How to Use

1. Enter a decimal number (e.g. 0.75, 1.333, or -2.5).
2. Click Convert.
3. The tool shows the exact fraction, the simplified fraction (if reducible), and the mixed number form if the value is greater than 1.

How It Works

The algorithm counts the decimal places in the input, then expresses the number as numerator / 10^n. For example, 0.75 has 2 decimal places: 75/100. The numerator and denominator are then divided by their greatest common divisor (GCD) to produce the simplified form: 75/100 ÷ 25/25 = 3/4. For mixed numbers, the whole part is the floor of the simplified fraction and the remainder is the numerator modulo the denominator.

Exact vs. Approximate Results

Terminating decimals (those with a finite number of digits after the decimal point) always convert exactly: 0.125 = 1/8. Repeating decimals like 0.333... are an approximation when entered with finite digits — 0.333 = 333/1000, not 1/3. To get the true fraction for a repeating decimal, enter the full repeating pattern manually if you know it (e.g. treat 1/3 as 0.33333333 for a close approximation).

Frequently Asked Questions

What is a mixed number?

A mixed number combines a whole number and a proper fraction, e.g. 1 3/4 instead of 7/4. It is shown when the simplified fraction is an improper fraction (numerator greater than denominator).

Why does 0.1 + 0.2 not equal 0.3 exactly in the tool?

JavaScript uses IEEE 754 floating-point arithmetic, so 0.1 + 0.2 = 0.30000000000000004. Enter 0.3 directly for the clean fraction result.

Is this free?

Yes, entirely free with no signup required.