Long division, with every step on show
Long division is the disciplined way to answer how many times one number fits into another — and what is left over when it does not fit exactly. The number being divided is the dividend, the number doing the dividing is the divisor, the whole-number answer is the quotient, and whatever remains is the remainder. This calculator gives all three useful forms of the answer at once: the quotient and remainder for sharing-and-leftovers problems, the decimal expansion rounded to exactly the number of places you choose for measurement-and-money problems, and a step panel showing each stage of the working with your own numbers, the way it would be written in a school exercise book.
The running example makes the three forms concrete. Dividing 1000 by 7: 7 fits into 1000 a whole 142 times, because 142 × 7 = 994, leaving a remainder of 6. Kept as a decimal, the division continues past the point — the remainder 6 becomes 60 tenths, 7 fits 8 times, the new remainder 4 becomes 40, and so on — giving 142.8571… to four places, where the digits 857142 actually repeat forever, a little cycle hiding inside sevenths that also appears in 1/7, 2/7 and every other seventh, each starting at a different point of the same loop. The step panel reproduces that bring-down-a-zero rhythm one decimal place at a time.
The method, and the convention this page states openly
Each long-division step asks one question — how many whole times does the divisor fit into what is currently on the table — writes that digit, multiplies back, subtracts, and brings down the next digit (or a zero past the decimal point). This page states its sign convention openly, because it matters for negatives: the whole quotient is truncated toward zero, and the remainder is defined as dividend minus quotient times divisor, so the check in the breakdown always reconstructs the dividend exactly, and the remainder takes the dividend's sign. Some textbooks instead floor the quotient, which changes the remainder's sign convention; neither is wrong, but a calculator should say which one it uses — so this one does.
Quotient-and-remainder or decimal: choosing the right form
The two forms answer different real questions, and part of division fluency is knowing which is being asked. Sharing 1000 sweets among 7 children is a quotient-and-remainder problem: 142 each, 6 left over, and the remainder's fate — a raffle, a rotation, the teacher's desk — is a human decision the arithmetic deliberately leaves open. Splitting a 1000-unit quantity into 7 equal measured parts is a decimal problem: about 142.8571 units each, and the rounding to your chosen places decides how much total error the rounding smuggles in, which is why places here run from 0 up to 10. The Fraction Calculator offers the third form of the same answer: as an exact fraction, 1000/7 simplifies not at all but converts honestly, and for longer expressions combining divisions with other operations the Scientific Calculator takes over.
Remainders are information, not failure
School exercises sometimes make a remainder feel like an unfinished answer, but remainders run the world: clocks are remainders after dividing hours by 12, weekdays are remainders after dividing days by 7, and the check digit on a bank card is a remainder in disguise. Division by zero, the one input this page refuses, deserves its refusal to be understood rather than memorised: asking how many times zero fits into a number asks for a count that would have to satisfy quotient times zero equals the dividend, and no such count exists for a non-zero dividend, while for zero itself every count would work — so the operation is undefined in both cases, and the calculator says so plainly.
Worked example
1000 divided by 7: the whole quotient is 142 (142 × 7 = 994), the remainder is 6, and the decimal to 4 places is 142.8571. The check always holds: 142 × 7 + 6 = 1000.
How to use this calculator
- Enter the dividend — the number being divided.
- Enter the divisor — it must not be zero.
- Choose the decimal places, from 0 to 10, for the decimal form.
- Read the decimal in the green panel, and the quotient and remainder in the breakdown.
- Follow the step panel: each decimal digit is produced by bringing down a zero and dividing again.
From long division to recurring decimals
Keep dividing past the places this page shows and one of two things always happens: the remainder becomes zero and the decimal terminates, as with quarters and eighths, or a remainder repeats and the digits from that point cycle forever, as with the sevenths above. Which fate a fraction meets depends only on its denominator in lowest terms — primes factors of 2 and 5 alone mean a terminating decimal in base ten, anything else means a repeat. That is why thirds are the famous nuisance of measurement, and why exact fraction forms, available from the Fraction Calculator, never lose the information that any finite decimal, however many places you choose here, eventually must.