An experimental tool to find the rational approximation of decimal and rational numbers, specifying the maximum numerator and denominator (in digits, bits or maximal value).
(Let us limit the numerator and denominator to three digits).
| Input | Rational Approximation |
|---|---|
| 0.12345 | 119 / 964 |
| 1234 / 5678 | 153 / 704 |
The program supports repeating (recurring) decimals using the “( )” notation, as well as exponents:
| Input | Rational Approximation |
|---|---|
| 0.(3) | 1 / 3 |
| 0.12(345) | 10 / 81 |
| 0.8(9) | 9 / 10 |
| 1.234e-4 | 617 / 5 |
If the input number is too close to zero or too large, and the maximum number of digits is insufficient, then the result may include an exponent, for example:
| Input | Rational Approximation |
|---|---|
| 1.2345e-7 | 458e-7 / 371 |
| 1234567/89 | 799e+4 / 576 |
The program also accepts the name of some common constants:
| Input | Rational Approximation |
|---|---|
| pi | 355 / 113 |
| e | 878 / 323 |
(The approximate values of these constants consist of 1000 digits).
As an experimental feature, the program also supports non-periodic continued fractions:
| Input | Rational Approximation |
|---|---|
| [5; 6, 7, 8] | 919 / 178 |
The program runs in this environment:
- Windows 11 or Windows 10 (64-bit),
- .NET 9.
To use it, download and unzip the latest archive from the Releases section. Launch the RationalApproximation executable.
Alternatively, the program can be compiled in Visual Studio 2026. The “.NET desktop development” workload is required. The source files can be got from the Releases section. The program is made in C#, WPF.
- Wikipedia contributors. Farey sequence — https://en.wikipedia.org/wiki/Farey_sequence
- Cook, John D., Rational approximation to a decimal number — https://www.johndcook.com/rational_approximation.html