Calculator
Exact quotient
–
Rounded result
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Computation steps
Example data table
Use these examples to test rounding combinations quickly.
| Dividend | Divisor | Target | Param | Mode | |
|---|---|---|---|---|---|
| 22/7 | 1 | dp | 3 | half_even | |
| 355/113 | 1 | sf | 5 | half_up | |
| 10 | 3 | dp | 0 | half_down | |
| -17 | 4 | step | 0.5 | toward_zero | |
| 2.75 | 0.2 | step | 0.25 | away_from_zero | |
| -5 | 2 | dp | 2 | up | |
| 1 | 8 | sf | 3 | down |
Dataset (append results)
| # | Dividend | Divisor | Target | Param | Mode | Exact | Rounded |
|---|
Formulas used
Quotient: q = a / b, with b ≠ 0.
Decimal places: round(q, dp) = toDecimalPlaces(q, dp, mode).
Significant figures: round_sf(q, s) = toSignificantDigits(q, s, mode).
Nearest step: round_step(q, h) = h × round(q / h, 0, mode).
Modes:
- Half up: ties go away from zero.
- Half to even: ties go to the nearest even.
- Half down: ties go toward zero.
- Down: toward −∞ (floor).
- Up: toward +∞ (ceiling).
- Toward zero: truncate fractional part.
- Away from zero: always increase magnitude.
How to use this calculator
- Enter a dividend and a divisor (fractions or decimals).
- Choose the rounding target: decimal places, significant figures, or step.
- Set the corresponding parameter: dp, sf, or step.
- Select a rounding mode to handle direction or midpoint ties.
- Press Calculate to see the exact quotient, rounded result, and steps.
- Optionally Add to dataset, then export CSV or PDF.
Rounding modes comparison (ties and negatives)
Illustrative outcomes for tie cases and signs; useful when choosing policy.
| Value | Target | Param | Half up | Half to even | Half down | Down (floor) | Up (ceiling) | Toward zero | Away from zero |
|---|---|---|---|---|---|---|---|---|---|
| 2.5 | dp | 0 | 3 | 2 | 2 | 2 | 3 | 2 | 3 |
| -2.5 | dp | 0 | -3 | -2 | -2 | -3 | -2 | -2 | -3 |
| 2.75 | step | 0.5 | 3.0 | 3.0 | 2.5 | 2.5 | 3.0 | 2.5 | 3.0 |
Note: step rounding computes k = q / h, rounds k per mode, then returns h×k.
Error metrics for rounded quotients
After rounding, quantify deviation using absolute and relative error. For quotient q and rounded value r:
- E_abs = |q − r|
- E_rel = E_abs / |q|, %E_rel = 100 × E_rel
| Dividend / Divisor | Target | Param | Mode | Exact q (≈) | Rounded r | |q − r| | % relative error (≈) |
|---|---|---|---|---|---|---|---|
| 22/7 | dp | 2 | half_even | 3.142857 | 3.14 | 0.002857 | 0.0909% |
| 355/113 | sf | 5 | half_up | 3.14159292 | 3.1416 | 0.00000708 | 0.000225% |
| 10/3 | step | 0.05 | half_even | 3.333333 | 3.35 | 0.016667 | 0.5000% |
Values are rounded for display; compute precisely in the calculator for your case.
Worked examples across targets
Quick reference showcasing different targets and modes on representative inputs.
| Dividend | Divisor | Target | Param | Mode | Rounded result (≈) | Notes |
|---|---|---|---|---|---|---|
| 22/7 | 1 | dp | 3 | half_even | 3.143 | Eight in 4th decimal rounds 3.142 → 3.143 |
| 355/113 | 1 | sf | 5 | half_up | 3.1416 | Five significant figures on high-precision ratio |
| 10 | 3 | dp | 0 | half_down | 3 | Below 3.5 so rounds down to 3 |
| -17 | 4 | step | 0.5 | toward_zero | -4.0 | k = -8.5 → toward zero gives -8 → ×0.5 = -4.0 |
| 2.75 | 1 | step | 0.5 | away_from_zero | 3.0 | Tie at 0.5 step goes away from zero |
FAQs
You divide two numbers to get a quotient, then apply a rounding rule—by decimal places, significant figures, or nearest step, with a chosen tie-breaking mode.
For finance, half to even reduces bias. For measurements, half up is common. Use step rounding for prices or increments like 0.05.
Decimal places control digits after the decimal point. Significant figures control total meaningful digits, improving consistency across very large or very small numbers.
Modes like up and down reference +∞ and −∞. Toward zero truncates; away from zero increases magnitude regardless of sign.
Division by zero is undefined. The calculator blocks calculation and asks you to provide a nonzero divisor.