Rounding & significant figures

There is no single correct way to round — there are several conventions, and which one you want depends on whether you care about the individual value or the sum of many of them.

Half up versus half to even

“Round half up” always sends a tie away from zero: 2.5 becomes 3. It is simple, and it is what everybody is taught. But it is biased: over many values, ties always push the total upward.

Banker's rounding sends ties to the nearest even digit: 2.5 becomes 2, and 3.5 becomes 4. Half the ties go up and half go down, so the bias cancels. This is why it is the IEEE-754 default and why accounting and statistical software use it.

Significant figures

Significant figures track precision rather than position. Leading zeros never count; trailing zeros after a decimal point do. 0.00420 has three significant figures. When multiplying or dividing, the answer carries the significant figures of the least precise input — a measurement is never made more accurate by arithmetic.

Do not round twice

Rounding 2.44 to one decimal gives 2.4, then to zero gives 2. Rounding 2.44 straight to zero gives 2 as well — but 2.45 → 2.5 → 3 versus 2.45 → 2 shows the trap. Always round once, from the original value.