Decimal places, significant figures, nearest multiple, up, down — plus banker’s rounding, which is why spreadsheet totals sometimes differ.
Round 0.5, 1.5, 2.5, 3.5, and 4.5 the school way and they become 1, 2, 3, 4, 5 — summing to 15. The true sum of the originals is 12.5. Round the same five values half-to-even instead and they become 0, 2, 2, 4, 4 — summing to 12, much closer to the true 12.5. Every individual answer moved by the same half-unit either way; only banker's rounding let some of those halves cancel instead of all stacking in the same direction.
Tie-breaking (half up versus half to even) is a decision about which way to round when a value sits exactly between two options. A completely separate problem is that computers cannot store every decimal exactly in binary in the first place — 0.1 and 0.2 each carry a tiny representation error before any rounding rule even runs, which is why 0.1 + 0.2 computed in most software returns 0.30000000000000004 instead of a clean 0.3. The first problem is about a choice; the second is about what a number can even be stored as. Rounding the display is a fix for the second problem — it hides representation error without removing it from the underlying calculation.
This page's own default, 2.5 rounded to the nearest 5, gives 5 — ties in this mode always round up, the ordinary school rule, not half-to-even. That is a different result in spirit from the dedicated half-to-even field just above it, which takes the same 2.5 to 2. Neither is a bug: rounding to a nearest multiple and rounding to a decimal place are different operations with independent tie rules on this page, and it is worth checking which rule a given field actually uses before assuming every "round" button on a page behaves the same way at an exact tie. Percentages get rounded just as often as currency — see the Percentage Calculator for that same arithmetic applied to shares of a whole — and for arithmetic that needs no rounding at all because it never leaves whole numbers, the Big Number Calculator keeps every digit exact regardless of size, and the Scientific Calculator is the better tool than this page for a calculation that needs full floating-point precision carried through to the end rather than rounded at every step.
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 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.
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.
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.
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.
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.
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.
For general arithmetic use the Basic Calculator, and for very large or very small magnitudes the Scientific Notation Calculator keeps significant figures visible. Percentage work is handled by the Percentage Calculator.