Python round() Mystery Explained: Why round(2.5) Doesn’t Round Up

Hi Pythonistas!

If you’ve ever used Python’s round() function, you might have noticed some surprising behavior when rounding numbers that are exactly halfway between two integers. For instance:

code

>>> round(1.5)
2
>>> round(2.5)
2

You might expect round(2.5) to return 3, but instead, it returns 2. What’s going on?

The Mystery of Bankers' Rounding

Python’s round() function follows a rule called “round half to even” or “bankers' rounding”. This rounding method ensures that for values ending in .5, the number is rounded to the nearest even integer, not always to the next integer up.

Why does it do this? The logic behind bankers' rounding is statistical. If we always rounded up from .5, it would introduce a subtle bias in calculations, which can become significant in certain scenarios. Rounding half to even helps to balance out these rounding errors.

Breaking It Down with Examples

Let’s look at some examples to see this rule in action:

code

>>> round(1.5)   # 1.5 rounds to the nearest even integer, which is 2
2
>>> round(2.5)   # 2.5 also rounds to the nearest even integer, which is 2
2
>>> round(3.5)   # 3.5 rounds to 4, as 4 is the nearest even integer
4
>>> round(4.5)   # 4.5 rounds to 4 for the same reason
4

Why Use Bankers' Rounding?

Imagine we have a large dataset where we repeatedly round halfway numbers. By using bankers' rounding, Python ensures that the errors average out, leading to more accurate results across many calculations. Financial institutions, scientific computations, and statistical applications often use this method to maintain fairness and accuracy in their calculations.

Python’s default rounding behavior may seem a bit unusual at first, but it’s grounded in statistical fairness. Bankers' rounding balances out rounding errors across large datasets, making it a helpful feature when precision and unbiased results are required.

Next time you round a number in Python, remember: .5 values will always go to the nearest even number, helping your calculations stay balanced and accurate!