An experimental tool that converts decimal and rational numbers to continued fractions, and vice versa. The program also displays the convergents, and converts the simple continued fractions to regular ones.
For example:
| Entered number | The result |
|---|---|
| 12.34 | [ 12; 2, 1, 16 ] |
| 5/6 | [ 0; 1, 5 ] |
| 0.8(3) | [ 0; 1, 5 ] |
| Entered continued fraction | The result |
|---|---|
| [ 12; 2, 1, 16 ] | 12.34 |
| [ 0; 1, 5 ] | 0.8(3) |
The program accepts various kinds of numbers:
| Input | Meaning |
|---|---|
| 123 | Integer number |
| 12.34 | Decimal number |
| 0.8(3) | Repeating (recurring) decimal |
| 5/6 | Fraction |
| 1.2e‑7 | Scientific notation (1.2×10⁻⁷) |
| pi | Number π ≈ 3.1415926 (1000 digits) |
| e | Euler's (Napier's) number e ≈ 2.7182818 (1000 digits) |
Converting a decimal or rational number to regular continued fraction:
Converting a simple continued fraction to decimal and rational number. The output also includes the corrected regular continued fraction:
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 ContinuedFractions 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.
- Dr Ron Knott, An introduction to Continued Fractions — https://r-knott.surrey.ac.uk/Fibonacci/cfINTRO.html
- Conrad, K., Negation and Inversion of Continued Fractions — https://kconrad.math.uconn.edu/blurbs/ugradnumthy/contfrac-neg-invert.pdf