Decimal to Fraction Calculator
Last updated: November 5, 2026
Convert a decimal number into a simplified fraction using an adjustable precision limit.
Simplified fraction
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- Approximation as a decimal: —
- Absolute approximation error: —
- Mixed-number form: —
On this page
Quick summary: Convert a decimal number into a simplified fraction using an adjustable precision limit.
Read the method, example and limitations
Updated reference sections in this guide are in English.
Guide language: English. Updated October 15, 2026.
What this calculator estimates
Convert a decimal number into a simplified fraction using an adjustable precision limit.
Inputs and units
Enter Decimal value, Maximum denominator. Use the units shown. Required fields cannot be blank. Use zero only where that field and the model allow it. Select Calculate after changing the values.
Method and assumptions
Search integer denominators up to the requested bound, capped at 100,000. For each denominator, select the nearest integer numerator and retain the smallest absolute error, then reduce by the greatest common divisor. The mixed-number output retains the original sign.
Worked example
-0.625 converts exactly to -5/8. It is a negative proper fraction, so its mixed-number display remains -5/8, not a positive 0 5/8.
Limitations
Some decimal inputs are approximations to repeating fractions. The displayed error measures the approximation used. A denominator search limit is not a guarantee of recovering an intended exact fraction from every rounded decimal.
A bounded approximation, not an exact decimal expansion
The search chooses a close fraction whose denominator is at most the entered limit, up to 100,000. For 0.333333 with limit 100, 1/3 is close but differs by about 0.000000333333. A repeating fraction can therefore be a better short representation without being identical to the input. The approximation-error output quantifies the difference; component-size limits protect integer precision.