Fraction arithmetic
Add, subtract, multiply or divide fractions and mixed numbers. See exact simplified results, common denominators and each calculation step.
Decimal to fraction converter with exact reduction
Turn a finite decimal into its exact simplified fraction. This converter treats the digits you enter as a decimal string, rather than rounding through a floating-point number. It also accepts scientific notation such as 1.25e-3.
Free to use, with no sign-in. Inputs and results stay in this page and are not sent with the form. Download a result before leaving; this tool does not save your work.
Worked result
0.375 = 3/8 exactly.
- Three decimal places give denominator 1000.
- Divide numerator and denominator by their greatest common divisor, 125.
- The reduced numerator is 3 and denominator is 8.
Convert 0.375 into a fraction
The decimal has three places after the point. Write it over one thousand, then remove the common factor.
0.375 = 375/1000
gcd(375, 1000) = 125
375 ÷ 125 = 3
1000 ÷ 125 = 8
Answer: 3/8This equality is exact for the entered decimal. Entering 0.333 produces 333/1000, not 1/3: the missing repeating digits cannot be inferred.
Place value supplies the denominator
A decimal with k digits after the point is an integer divided by 10^k. Scientific notation shifts that decimal position by its exponent before reduction. The sign stays with the numerator.
Remove leading zeros when interpreting magnitude, but count all decimal places in the input representation. Trailing zeros may create a larger initial denominator; greatest-common-divisor reduction removes them from the final fraction.
digits × 10^(exponent − decimal_places)
If exponent − decimal_places < 0:
fraction = signed_integer_digits / 10^(decimal_places − exponent)Input limits and common mistakes
Only finite decimals are accepted. Use a dot as the decimal separator, and an optional e exponent. Percent signs, commas, units, fractions and repeating-decimal notation are rejected.
The mantissa is limited to 256 digits and the exponent to ±300. Inputs such as 1e-300 remain exact fractions. A finite decimal is not evidence that a measured physical quantity is known to that precision.
Questions about decimal to fraction
What fraction is 0.125?
It is 125/1000, which reduces by a factor of 125 to 1/8.
What happens to trailing zeros?
0.3750 and 0.375 both reduce to 3/8. The different written precision is not retained as a measurement uncertainty.
Can I convert 0.333… to 1/3?
Not with this finite-decimal tool. Enter 1/3 in the fraction calculator when the repeating value is known exactly.
Sources and verification
These references explain the formulas or formats. The worked examples above were created for this tool and checked against independent calculations or format round trips. AI-assisted development does not imply a named human expert review.
- OpenStax: decimals and fractions — Decimal place value and fraction conversion.
Published 2026-10-23. Examples are illustrations, not measurements of a service or claims about search rankings.
Related tools
Compare and order fractions
Compare two or more fractions, decimals and mixed numbers. Order them exactly and see the common-denominator explanation.
Scientific notation
Convert a finite decimal or e notation into normalized scientific notation and an exact decimal expansion without rounding the entered digits.
Further reading
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