Exact Rational Representation Workbench

How to use Exact Rational Representation Workbench

Repeating cycles use exact powers-of-ten subtraction; long division identifies a repeated remainder. Approximation uses continued-fraction convergents and a final semiconvergent, comparing exact rational errors under the denominator cap. Equal-error ties prefer the last complete convergent.

1. Enter decimal, such as0.1(6) or3.14159, integer numerator for fraction mode, integer denominator for fraction mode, maximum approximation denominator.
2. Choose the stated convention and check the units and supported model.
3. Calculate, inspect the result, then copy or download it.

Good to know

• Up to100digits per source integer/decimal, no exponent expressions, nonzero fraction denominator, output cycle up to10000digits. Approximation denominator1–1million;8192-bit rational intermediates. Existing fraction arithmetic remains a related separate task.
• Runs locally. Text/JSON fields are capped at30,000 characters; stricter page-specific and numeric-string limits also apply. Numeric inputs are bounded to magnitude1e15 and nonzero magnitude at least1e-100 unless an exact-string mode states otherwise. Approximate summaries use12 significant digits; CSV numeric cells retain the complete stored value and potentially formula-like string cells gain a protective apostrophe; unsupported, non-finite or detected underflow states return an error.