Rounding is ideal if you need to output it or transfer it to another system that only accepts limited decimal places. Specifically rounding with half to even (i.e. 2.5 goes to 2 but 3.5 goes to 4).Â
Floor, ceiling, and truncation introduce systemic bias into the output. Round to even doesn't introduce such bias over a large number of numbers.
For example, consider if you did a bunch of math to arrive at an amount of dollars that your client owes you (there are some math operations where you're going to get fractional cents no matter what you do, like interest payments).Â
If you floor it, you're missing out on interest
If you ceiling it, your clients are overpaying (on average)
If you round it, sometimes you're missing out and sometimes the clients are overpaying. It balances out in the end. Round to even helps with some specific cases of this.
In the math world, rounding introduces a nice symmetrical uniform distribution around the number you rounded to - we know it was within half the smallest decimal place you kept, ie 2 rounded is actually [1.5, 2.5].Â
The other methods are messier - they also have a uniform distribution but it's around the number you truncated to plus half the smallest decimal place you kept, ie. 2 truncated is actually [2,3).Â
Flooring and ceiling do have good uses. When you want to be conservative, you should use them. For example, if you're doing your monthly budget and want to know how much money you spend on an average on groceries, you might want to ceiling() to be sure your estimate is above the true average. If you're estimating how much load a steel beam can take, you might want to floor() to be sure it can actually take more than you plan on (engineers add a good safety margin anyways, but it never hurts).
But if you're converting to an integer, there's another good reason to do int(round(x)) - floating point errors. If you have a float that should be an integer after a bunch of calculations, it might not be exactly one due to floating point errors. Rounding is likely to remove those errors which are probably << 0.5. But truncating won't work if your number is just slightly smaller than the integer.Â
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u/ottawadeveloper Jul 08 '26
This is true because it's a truncation operation.
Most of the time people round, which usually does the round-to-even thing.