Round it five different ways, and see why they disagree.

The tie-break is where methods diverge

Every rounding method agrees on 2.4 and 2.6. They differ only on exact halves, and that difference compounds.

Half up — the school rule. 2.5 → 3, 3.5 → 4. Simple, and biased: it rounds ties upward every time, so summing many rounded values drifts high.

Banker's rounding — half to even. 2.5 → 2, 3.5 → 4. Ties go to whichever neighbour is even, so they split roughly evenly between up and down and the bias cancels over many values.

This is not academic. It is the IEEE 754 default and the reason a spreadsheet total can differ by a cent or two from one you rounded by hand — and why financial and statistical software prefers it.

Decimal places versus significant figures

Decimal places count digits after the point. Significant figures count meaningful digits from the first non-zero one, wherever the point sits.

0.004567 to 2 decimal places is 0.00 — the information is gone. To 2 significant figures it is 0.0046, which preserves the magnitude. That is why scientific work uses significant figures: they track precision rather than position, and they survive a change of units.

Rounding to a nearest multiple

Useful well beyond decimals: to the nearest 5 for a tip, the nearest 50 for a budget, the nearest 0.25 for a timesheet. The rule is the same — divide, round, multiply back.

One caution worth knowing: never round twice. Taking 2.44 to 2.4 and then to 2 gives a different answer from rounding 2.44 straight to 2. Always round once, from the original.

What is banker’s rounding and why does it exist?

It rounds exact halves to the nearest even number rather than always up — 2.5 becomes 2, 3.5 becomes 4. Because ties split roughly evenly between up and down, the upward bias of the school rule cancels out across many values. It is the IEEE 754 default and standard in financial and statistical software.

What is the difference between decimal places and significant figures?

Decimal places count digits after the point; significant figures count meaningful digits starting from the first non-zero one. 0.004567 to 2 decimal places is 0.00, losing everything, while to 2 significant figures it is 0.0046.

Why do my rounded numbers not add up to the rounded total?

Because rounding each value and summing is not the same as summing and rounding once. The individual errors accumulate. Financial systems handle this by tracking the residual and assigning it to one line, so the parts still reconcile to the whole.

Should I round intermediate results in a calculation?

No. Carry full precision through and round only the final answer. Rounding at each step compounds the error, and rounding an already-rounded number can give a different result from rounding the original once.