Rounding & error bands | Intermediate vs final

Where to round

The same rounding place and method apply to both tabs.

Rounding method Keep trailing zeros Teacher mode

Rounded result

Original vs rounded value with error band.

We highlight both the place you round to and the digit you look at for the rounding decision.

A

First operator

B

Second operator

C

Rounding points Round inputs first (A,B,C) Round the intermediate (A op1 B)

Use the shared rounding settings above. Both scenarios use the same place and method so the comparison stays fair.

Difference (B−A):

Why do they differ?

If you round midway, the rounding error is carried into the next operation and can accumulate or amplify.

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 C templates.
Copy a shareable URL or LaTeX, download the error-band SVG, and switch to teacher mode.

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.