The same rounding place and method apply to both tabs.
Rounded result
Original vs rounded value with error band.
Digit inspected
We highlight both the place you round to and the digit you look at for the rounding decision.
Steps
What you can do
- Round to any decimal or integer place, with the digit you inspected highlighted.
- See the maximum error and the possible true-value band on a number line.
- Compare intermediate vs final rounding on
(A op1 B) op2 Ctemplates. - Copy a shareable URL or LaTeX, download the error-band SVG, and switch to teacher mode.
How to use this calculator effectively
Use this page to round a value and understand the maximum error band introduced by that rounding choice.
How it works
The calculator applies the selected rounding rule at the requested place, then reports the rounded value, absolute error band, and relative error when a reference value is available.
When to use
Use it for measurement reporting, significant-figure checks, lab notes, and classroom examples where the displayed precision should match the actual tolerance.
Common mistakes to avoid
- Rounding intermediate values before the final answer.
- Confusing decimal places with significant figures.
- Reporting more digits than the measurement supports.
- Comparing rounded values without carrying the error band forward.
Interpretation and worked example
Rounding 12.34 to one decimal gives 12.3 with a half-unit band of 0.05 at that decimal place. If the error band is too large for your use case, keep more digits or revisit the measurement precision.
See also
FAQ
Which digit do I look at when rounding to the nth decimal?
Look at the digit one place to the right of where you round. If it is 5 or more, round up; otherwise round down.
How do I round to the nearest ten?
Use the ones place as the decision digit. For example, 368 becomes 370 (error ±5).
How do I express the error range of an approximation?
With half-up rounding, half of the unit is the maximum absolute error. Rounding to 1 decimal gives ±0.05, so the true value is within that band.
Why does rounding midway change the answer?
Once a rounded value is used in the next operation, its error can accumulate or be amplified, leading to a different final result.
How is rounding of negative numbers handled?
We use “away from zero” half-up. −1.5 becomes −2, while −1.25 becomes −1.
Is my input sent to a server?
No. Everything runs locally in your browser, including the charts.