Divide signed integers and finite decimals exactly as rational numbers, with rounded or repeating labels and a real step-by-step long-division walkthrough.
01 / EXACT DECIMAL INPUTS
Enter signed integers or finite decimals. Results and steps use exact decimal-string/BigInt arithmetic, not floating-point fractions.
02 / QUOTIENT & EXACT FORM
Both magnitudes are already integers; no decimal scaling is needed. The final quotient is nonnegative.
25
───
5 ) 125
−10
──
2
25
−25
──
0The quotient is aligned above the dividend. Read down: subtract the divisor × quotient digit, keep the remainder, then bring down the next digit. Decimal columns stay aligned; leading quotient zeros are omitted and internal zeros are retained. Exact result: 25.
Exact or expanded notation: 25. Parentheses mark a repeated block when its cycle is found.
1. Integer place 1: bring down 1. Quotient digit 0 (leading zero not written).
2. Integer place 2: bring down 2. Quotient digit 2.
3. Integer place 3: bring down 5. Quotient digit 5.
The fractional-step limit is max(20, display precision + 1), up to 51 digits; steps stop earlier at zero or a repeated remainder. Integer remainder uses A = q × B + r, truncation toward zero and the dividend’s sign; it is shown only when both original operands are integers.
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Enter a dividend and nonzero divisor. Choose decimal display precision, inspect exact fraction/remainder results and expand the bounded, copyable long-division steps.
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Yes. Signed finite decimal strings are parsed into BigInt-backed rational numbers rather than binary floating-point values. The exact simplified fraction is retained even when the displayed quotient is rounded.
The reduced denominator determines whether a decimal repeats: after removing factors of two and five, any remaining factor implies a repeating expansion. Displayed decimals round half away from zero at the selected precision. A repeating result is never described as an exact finite decimal.
They are shown when both original inputs represent integers. The quotient truncates toward zero and a nonzero remainder keeps the dividend’s sign, satisfying A = q × B + r. Decimal operands instead use the exact rational quotient; scaled walkthrough remainders are not mislabeled as original integer remainders.
Both operands are multiplied by the same power of ten to make them integers. Their magnitudes are divided digit by digit; each brought-down digit, quotient digit, subtraction and remainder is computed exactly. A negative sign is applied to the final quotient when appropriate.
Yes. The walkthrough marks leading zeros that are not written, retains internal zeros such as the zero in 1005 ÷ 5 = 201, and brings down zeros after the decimal point. A repeated remainder identifies a cycle, shown with parentheses when fully found.
Each operand supports at most 60 digits and 30 decimal places within 64 characters. The fractional-step limit is max(20, selected precision plus one), at most 51; generation stops sooner at zero or a repeated remainder. Long lists are paginated and truncation is disclosed. Scientific notation and commas are not accepted; division by zero is undefined.