Rounding modes explained
Half up, bankers, ceiling, floor, and truncation compared, with worked ties and the sign rules that trip people up on negatives.
The problem of the tie
Rounding is easy until a value lands exactly on a half, like 2.5 or -0.5. At that point you must choose a direction, and different fields have settled on different answers. A rounding mode is simply the rule for breaking that tie, plus the rule for which way non-ties go. Picking the right mode matters most when you round many numbers, because a consistent bias in one direction quietly accumulates into a noticeable error across a whole column.
Half up versus bankers
Half up rounds every tie away from zero, so 0.5, 1.5, and 2.5 become 1, 2, and 3. It is the schoolbook rule and is easy to predict, but it nudges sums slightly upward because ties always climb. Bankers rounding, or round half to even, instead sends each tie to the nearest even integer, so 0.5 and 2.5 both go to 0 and 2 while 1.5 and 3.5 go to 2 and 4. Over a long list, roughly half the ties round up and half round down, which keeps totals closer to the true value. This is why accounting and many standards prefer it.
Directed rounding: ceiling, floor, truncate
The other three modes ignore the tie question and always move in a fixed direction. Ceiling rounds toward positive infinity, so both 2.1 and 2.9 become 3, while floor rounds toward negative infinity, sending 2.9 down to 2. Truncation drops the fractional part, which means it rounds toward zero and behaves like floor for positive numbers but like ceiling for negative ones. That last distinction is the classic trap: floor of -2.7 is -3, but truncating -2.7 gives -2.
Rounding to a step, not a place
Sometimes you do not want a number of decimals but a specific granularity, such as the nearest 5 cents, nearest 10, or nearest 0.25 inch. The Nearest multiple option handles this by scaling the value by the step, rounding the result with your chosen mode, and scaling back. Because the same five modes apply to the scaled value, you can, for example, always round a price up to the next 5 cents using ceiling, or snap a measurement to the closest quarter using half up.