Decimal to Fraction Converter
Turn a decimal into its simplest fraction and mixed number. Enter any decimal — positive or negative, like -0.75 — and choose how tightly to limit the denominator.
Example: with Decimal -0.75 · Accuracy Most accurate (den ≤ 10000) → Fraction: -3/4.
- Mixed number-3/4
- Check= -0.75 (exact)
Computed by the calculator below using its default values. Change any input to see your own numbers.
The tool searches denominators up to the chosen limit and keeps the fraction closest to your decimal, reduced to lowest terms. Terminating decimals like -0.75 come out exact (-3/4).
From decimal to fraction
Every terminating decimal is a fraction in disguise: 0.75 is 75/100, which reduces to 3/4. The reducing step is what turns an ugly ratio into a clean one — divide the top and bottom by their greatest common factor until nothing else divides evenly. A negative sign rides along untouched, so -0.75 becomes -3/4.
Repeating and irrational decimals cannot be written as an exact fraction with a small denominator, so this tool approximates them. It scans denominators up to your chosen limit and keeps the closest match, then reports whether the result is exact or rounded. That is how 0.3333 lands on 1/3 rather than a clumsy 3333/10000.
How it’s calculated
Denominator-limit method: the tool tests denominators d from 1 up to the limit (default 10,000), keeping the fraction round(fr×d)/d whose value is closest to the fractional part, and stops early when the error drops below 1e-12. The smallest qualifying denominator wins, so the fraction is already in lowest terms. The whole part is added back and the sign restored.
Repeating or irrational decimals are approximated to the denominator limit, not represented exactly. Raise the limit for a closer fit.
Common decimals as fractions
| Decimal | Fraction | Note |
|---|---|---|
| 0.5 | 1/2 | Exact |
| 0.25 | 1/4 | Exact |
| 0.375 | 3/8 | Exact |
| 0.75 | 3/4 | Exact |
| 0.3333… | 1/3 | Repeating |
| 0.1 | 1/10 | Exact |
Found by denominator-limit search; a repeating decimal like 0.3333… maps to 1/3.
Common mistakes
- Reading -0.75 as -75/100 and stopping — it reduces to -3/4.
- Expecting an exact fraction for a rounded decimal like 0.3333, which really represents 1/3.
- Raising the denominator limit and accepting an ugly fraction that is barely more accurate than a simple one.
Frequently asked questions
What is -0.75 as a fraction?
-3/4. Since 0.75 is 75/100, it reduces to 3/4, and the negative sign carries over to give -3/4.
How does the converter turn a decimal into a fraction?
It searches denominators up to your chosen limit and keeps the fraction closest to your decimal, then reduces it to lowest terms.
What is 2.25 as a fraction?
9/4, or 2 1/4 as a mixed number. The 0.25 part is 1/4, and two whole units add 8/4.
Why is my repeating decimal not exact?
A repeating decimal like 0.3333 needs an infinite expansion for a perfect fraction. The tool gives the closest fraction within the denominator limit, marking it approximate.