Long Division with Decimals Calculator
Visual long division solver for decimal numbers. Shows step-by-step decimal shifting and the complete subtraction grid for precise calculation.
About
Precise division involving decimals often trips up students and professionals alike. The primary challenge lies in the decimal point alignment. Incorrect placement changes the result by orders of magnitude. This tool eliminates that risk by automating the standard algorithm. It handles the initial decimal shift for both dividend and divisor. Users see the transformation from decimal division to integer division. This ensures the final quotient places the decimal point correctly. It serves structural engineers verifying load distributions or students mastering arithmetic concepts. The step-by-step grid exposes every subtraction and remainder.
Formulas
The core principle relies on the invariant property of division when scaling by powers of 10.
We determine k such that the divisor becomes an integer. The long division then proceeds as:
Reference Data
| Term | Definition | Visual Representation |
|---|---|---|
| Dividend | The number being divided. | 12.5 |
| Divisor | The number doing the dividing. | 0.5 |
| Quotient | The result of the division. | 25 |
| Remainder | Leftover amount if not exact. | r = 0 |
| Shift Logic | Multiplying by powers of 10. | 0.5 → 5 |
| Algorithm | Standard Euclidean Division. | a = bq + r |
| Precision | Decimal places calculated. | Up to 10 digits |
| Notation | Long Division Bracket. | )_____ |