Long Division Calculator
Divide numbers step by step with quotient, remainder and decimal expansion. Shows repeating decimals clearly.
Full result
62.5
Quotient
62
Remainder
0
Decimal part
0.5
Shown as quotient plus remainder, with the decimal expansion of the remainder.
Last updated: February 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
The full verification method is on our how we verify page. Found an error? Tell us and we will re-check it.
When to Use This Calculator
Long division is a core skill in Indian school mathematics, and this calculator supports both learning and real-world division problems. Students use it to verify their working while practising the division algorithm, especially when learning remainders and decimal expansions in Classes 4 to 8. Teachers generate practice examples with known answers for homework and tests. Everyday situations call for it too: splitting a box of sweets among children, dividing a group of students into equal teams, or distributing stationery across classes. Small business owners calculate how many full packs can be made from a bulk quantity, with the remainder showing the leftover stock. The tool also handles repeating decimals, helping students understand why 1 ÷ 3 gives 0.333... and never terminates. By showing quotient, remainder and decimal expansion together, it mirrors exactly how long division is taught in classrooms.
How to Use This Calculator
- Step 1: Enter the dividend, the number being divided, such as 500.
- Step 2: Enter the divisor, the number you divide by, such as 8.
- Step 3: Read the whole-number quotient and the remainder left over.
- Step 4: See the decimal expansion of the remainder, with repeating patterns flagged automatically.
Worked Example
A class teacher in Nagpur has 500 toffees to distribute equally among 8 children for the Republic Day celebration. She enters 500 as the dividend and 8 as the divisor. The calculator shows a quotient of 62 with a remainder of 4, so each child gets 62 toffees and 4 are left over. The decimal part then converts the remainder: 0.5, making the full answer 62.5. Her colleague checks 100 ÷ 4, which divides exactly with quotient 25 and no remainder. A third teacher tries 1 ÷ 3 and sees the calculator flag 0.3 as a repeating decimal, because the digit 3 repeats forever.
Tips and Common Mistakes
- •Tip 1: Check your division by multiplying the quotient with the divisor and adding the remainder back.
- •Tip 2: When the remainder is zero, the division is exact and the decimal part shows no digits.
- •Tip 3: Use the repeating flag to spot fractions that never terminate, like thirds, sixths and sevenths.
- ✗Mistake 1: Entering a divisor of zero, which is undefined and correctly rejected by the calculator.
- ✗Mistake 2: Ignoring the remainder, which matters in real problems like distributing items or grouping students where partial shares are not possible.
Frequently Asked Questions
How does long division work?
You divide the dividend by the divisor to get a whole-number quotient and a remainder. Any leftover remainder is then expanded as decimal digits, like 500 ÷ 8 = 62 with remainder 4, giving 62.5.
What is a repeating decimal?
Some divisions never end cleanly, such as 1 ÷ 3 = 0.3333... The calculator detects the repeating digit pattern and labels the result as repeating.
What is the difference between quotient and remainder?
The quotient is how many whole times the divisor fits into the dividend. The remainder is what is left over, always smaller than the divisor.
Can I use the long division calculator for decimals?
The calculator is built for whole numbers. Enter integers as the dividend and divisor; decimal or fractional inputs are not supported.
Why is long division still taught in schools?
It builds a deep understanding of how division and remainders work, which helps with fractions, ratios, remainders and mental arithmetic later on.
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