Long Division Calculator with Repeating Decimal Detection
Divide integers of arbitrary practical length using exact BigInt arithmetic. The calculator shows quotient and remainder, each whole-number long-division step and a decimal expansion with repeating-cycle detection.
Dividend and divisor
Long division result
long division calculator: formulas, interpretation and worked use
This long division calculator avoids floating-point rounding. It supports very large signed integers and detects recurring decimal remainders up to a selected digit limit.
Transparent calculation steps
The long division calculator displays the intermediate values used in the result so users can audit the calculation rather than receiving an unexplained answer.
Input validation and edge cases
Impossible, incomplete and non-finite inputs are rejected with a specific message. Boundary cases are handled explicitly instead of being silently rounded into a misleading result.
Units and precision
Where units apply, inputs are converted to a consistent internal basis before the formula is evaluated. Results retain enough precision for checking and are then formatted for practical reading.
Worked interpretation
The result panel separates the primary answer, supporting quantities and a formula trace. This makes the calculator suitable for checking homework, planning scenarios and comparing alternatives.
Whole-number steps
The step table follows the written algorithm digit by digit, recording the partial dividend, quotient digit and resulting remainder.
Decimal cycles
Each decimal remainder is stored with its digit position. When the same remainder reappears, the digits between positions form the repeating block.
Exact integer quotient and remainder
The long division calculator uses exact BigInt arithmetic for signed whole numbers beyond the ordinary JavaScript safe-integer limit. It reports the quotient truncated toward zero and a remainder consistent with dividend = divisor × quotient + remainder. The step trace follows successive partial dividends rather than converting the problem to floating-point division.
Decimal expansion and repeating cycles
The long division calculator can continue the remainder process into decimal places. When a remainder repeats, subsequent digits repeat from the same position, so the tool marks the recurring cycle. If no cycle or zero remainder is reached before the selected limit, the decimal is labeled truncated. Division by zero is rejected. Negative signs apply to the final value while the digit-generation process uses absolute magnitudes, preserving standard arithmetic identities.
Can it divide values larger than the safe integer limit?
Yes. Whole-number arithmetic uses BigInt.
How is a repeating decimal identified?
A repeated remainder means the subsequent decimal digits will repeat from that position.
What happens when the decimal limit is reached?
The displayed decimal is truncated and labeled unless the remainder has already reached zero or a cycle was detected.