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Continued Fraction Expansion

Expand one finite real value into a bounded simple continued fraction.

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Continued fraction calculator online

Expand one finite real value into a bounded simple continued fraction. Use this for the specific transformation described above. Start with the fixed sample and compare its result before replacing it with your own representative input.

How to use it

Enter a value or text in the format shown in the example. Set maximum terms. Choose Calculate. Review the output, then copy or download it.

Options and example settings

Option	Choices / value	Example default
Maximum terms	Enter maximum terms.	8

Worked examples

Use this for the specific transformation described above. Start with the fixed sample and compare its result before replacing it with your own representative input.

Reproducible worked example

Settings: Maximum terms: 8

Input:

3.141592653589793

With the input and settings above, the tool produces:

Output:

The example returns 8 top-level items in an array.

Limitations and common mistakes

Calculations use your supplied assumptions and floating-point arithmetic. Check input order, units and the worked example before relying on a result.
Combined input is bounded to 150,000 characters; output text is bounded to 1.2 million characters. Some algorithms impose smaller limits, stated in their error messages.

Frequently asked questions

What format should I enter?

Enter a value or text in the format shown in the example. The worked example shows the supported structure and actual output.

How can I expand a continued fraction online?

Enter a value or text in the format shown in the example. Set maximum terms. Choose Calculate. Review the output, then copy or download it.

Where is my input processed?

The bundled tool processes input in your browser. It does not upload tool input to a conversion service. Other site plugins, analytics, advertising and browser extensions may have separate behavior.