Most people learn 'Round Half Up' in elementary school: if the fractional part is 0.5 or greater, you round up to the next whole number. If it is less than 0.5, you round down. 2.5 becomes 3, and 2.4 becomes 2.
However, this method introduces a mathematical bias. Consider the digits 1 through 9. Four digits (1, 2, 3, 4) trigger a round down. Five digits (5, 6, 7, 8, 9) trigger a round up. If you apply this rule across a dataset of millions of transactions, your total sum will be artificially inflated because you are rounding up more often than you are rounding down.
The solution: Banker's Rounding (Round Half to Even)
To eliminate this upward bias, financial institutions and scientific computing systems use 'Round Half to Even', commonly known as Banker's Rounding. This is the default rounding mode in IEEE 754 floating-point standards, meaning it is the default behavior in languages like Python and C#.
In Banker's Rounding, if the number is exactly halfway between two integers (ending in .5), it rounds to the nearest EVEN integer. So, 2.5 rounds down to 2, but 3.5 rounds up to 4. Over a large dataset of random numbers, half of the .5 values will round up and half will round down, perfectly neutralizing the statistical bias.
When to use Ceiling and Floor
Beyond rounding to nearest, algorithms frequently use strictly directional rounding: Ceiling (always round up) and Floor (always round down). These are used when partial units cannot exist logically in the real world.
For example, if a bus holds 40 people and you need to transport 85 people, 85 / 40 = 2.125. Standard rounding would suggest 2 buses. But you cannot leave 5 people behind. You must apply a ceiling function to 2.125, resulting in 3 buses. Conversely, floor rounding is often used in age calculations; you remain 21 until the exact day you turn 22, no matter how close you are to your birthday.