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Step-by-step
CSV/PDF export
Classic bracket
Result
Classic Bracket Diagram (integer + decimals)
Step-by-Step Long Division Log
| # | Brought down | Partial dividend | Quotient digit | Product (digit × b) | Remainder | Phase |
|---|
Example Data
| Dividend (a) | Divisor (b) | Precision | Rounding | Action |
|---|---|---|---|---|
| 789.25 | 23 | 10 | round | |
| 1000 | 8 | 8 | truncate | |
| -355 | 113 | 12 | round | |
| 12.5 | 0.4 | 6 | truncate |
Formula Used
Long division satisfies the identity a = b·q + r with the Euclidean remainder constraint 0 ≤ r < |b|. For decimal expansion, we continue the algorithm by bringing down zeros to the remainder to obtain digits after the decimal point.
- Integer mode uses Euclidean division to ensure a non-negative remainder smaller than |b|.
- Decimal mode computes additional digits by repeatedly multiplying the remainder by 10 and dividing by |b|.
- Rounding mode “round half up” rounds the final kept digit using the next discarded digit.
How to Use
- Enter the dividend (a) and divisor (b). Non-integer and negative values are supported.
- Choose decimal places and rounding. Select “Integer quotient and remainder” to emphasize a = b·q + r.
- Toggle diagram settings for decimals and zero-digit steps as desired.
- Click Calculate. Review the step-by-step table and the summary verification.
- Use Export Steps CSV or Export Result PDF to download your work.
FAQs
We use the Euclidean remainder, which is always non-negative and strictly less than |b|, regardless of the signs of a and b.
After finishing the integer pass, if the remainder is non-zero, we repeatedly multiply it by 10, divide by |b|, and record each quotient digit.
Yes. We operate on absolute values for the manual steps, track the overall sign separately, and present the Euclidean remainder convention in integer mode.
Choose “Truncate” to cut after the chosen places, or “Round half up” to increase the last digit when the next discarded digit is 5 or more.
Multiplying both numbers by the same power of 10 preserves the ratio, letting us use integer long division accurately before extending digits after the decimal point.