Find the Decimal Expansion of a Number

Every rational number p/q has a decimal expansion - the base-10 spelling of its value. Some are short and clean (1/2 = 0.5), others end in a forever-repeating cycle (1/3 = 0.333..., 1/7 = 0.142857142857...). Knowing which is which, and exactly what the recurring block is, is one of the oldest results in arithmetic, and long division reveals both in one pass.

Find the Decimal Expansion runs exact long division on any numerator and denominator: it reports the integer part, marks the recurring block with parentheses - 0.(285714) - and shows the full expansion with no rounding at any size. Copy or download the exact representation.

• Exact long division: Remainders tracked, no floating point.
• Recurring block marked: 0.(142857) style output.
• Terminating detected: Stops naturally when the expansion ends.
• Integer part separated: The digits before the point, exact.
• Any size: BigInt arithmetic handles huge values.
• Copy or download: Export the expansion as text.

1. Enter a numerator - the p of p/q.
2. Enter a denominator - the q, never zero.
3. Generate - exact long division runs and the expansion prints.
4. Read the block - parentheses mark the repeating cycle.
5. Copy or download - the full expansion.

1. 1/2: 0.5 - terminating, two factors 2 and 5 only.

2. 1/3: 0.(3) - a single repeating 3 forever.

3. 1/7: 0.(142857) - the famous six-digit cycle.

4. 3/8: 0.375 - terminating, short and clean.

5. 22/7: 3.(142857) - the classic pi approximation, its exact expansion.

• Truly exact: Long division never rounds - the expansion is the real one.
• Block marked: Repeating cycles are shown, not guessed.
• Both kinds explained: Terminating and repeating each handled by the same division.
• Huge values fine: BigInt keeps every digit exact.
• Copy or download: The expansion exports one line.
• Private and free: All computation stays in the browser; nothing is uploaded or logged.