NUMBER LAB · EXPLORE WITH CONFIDENCE

Repeating Decimal & Fraction Explorer

Expand fractions into terminating or repeating digits in bases 2–36, reveal the repeating period and inspect long-division remainders.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

1/7 becomes 0.(142857), where parentheses identify the six repeating digits. In binary, 1/3 is 0.(01).

Scope and limits

Numerator and denominator up to 100 digits; bases 2–36; up to 3,000 fractional digits. An unfinished period is explicitly truncated, not rounded.

Calculations run in your browser. Projects are saved only when you download them. Website advertising and analytics follow the privacy and consent settings. Import large integer CSV columns as text in spreadsheets to preserve their digits.

Using Repeating Decimal & Fraction Explorer

Expand fractions into terminating or repeating digits in bases 2–36, reveal the repeating period and inspect long-division remainders.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

1/7 becomes 0.(142857), where parentheses identify the six repeating digits. In binary, 1/3 is 0.(01).

Questions & answers

What do parentheses mean?

The parenthesized block repeats indefinitely. An ellipsis instead means the selected digit limit was reached without finding the complete period.

Is the displayed expansion exact?

Terminating and detected repeating results are exact. A truncated prefix is not a complete representation and is clearly labeled.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.