An experimental tool to find the rational approximation of decimal and rational numbers, specifying the maximum size of nominator and denominator (in digits).
(Let us limit the nominator 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).
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 source files, which are got from the Releases section too, can be compiled in Visual Studio 2022 that includes the “.NET desktop development” workload. 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