Rounding calculator
Always rounding .5 upward introduces a small systematic bias, because half the time you round up and never down. Over a million transactions that bias becomes real money. Banker’s rounding sends .5 to the nearest even number instead. 2.5 goes to 2 and 3.5 goes to 4, so the bias cancels out. It is the default in most financial software and in the IEEE 754 floating-point standard your computer already uses.
Standard rounding sends 2.5 up to 3. Banker’s rounding sends it to 2, the nearest even number, so repeated rounding does not drift upward. Truncation simply drops the decimals, giving 2 for both 2.5 and 2.9.
How to round a number
Rounding twice is a trap worth knowing about. Rounding 2.44 to one decimal gives 2.4, and rounding that to zero gives 2, but rounding 2.44 straight to zero gives 2 as well. Try 2.45: to one decimal it is 2.5, and then to zero it is 3, whereas going directly gives 2. Always round once, from the original value, to the precision you actually need. Chained rounding is how a spreadsheet total ends up disagreeing with the sum of its displayed rows.
Questions
Three by standard rounding, two by banker’s rounding. Both are correct conventions.
Halves go to the nearest even number, so the upward bias of always rounding up cancels out over many values.
They agree for positive numbers. For negatives, floor goes down (−2.5 to −3) and truncate goes toward zero (−2.5 to −2).
Divide by 5, round, multiply back. Use the nearest-multiple field above.
Usually because displayed values are rounded but the underlying ones are not, or because values were rounded twice.