Quick guide
How to use this calculator
- Enter a finite decimal.
- Compare the truncation-based signed fraction with the floor-based non-negative fraction.
- Verify that either pair reconstructs the original number.
Calculation method
Negative values reveal the convention
Truncation removes the fractional digits toward zero. Floor chooses the lower integer, so its remainder is always at least zero and below one.
Worked example
Parts of −12.375
Both decompositions are exact but use different integer anchors.
−12.375 = −12 + (−0.375) = −13 + 0.625
Supported inputs
Precision and limits
Exact decimal input
Finite decimals use integer-scaled arithmetic, with no binary floating-point conversion.
Input boundary
Unless stated otherwise, use at most 200 digits total and 100 digits after the decimal marker.