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### Rounding Errors

Because floating-point numbers have a limited number of digits, they cannot represent all real numbers accurately: when there are more digits than the format allows, the leftover ones are omitted - the number is rounded.

### Example from Python Documentation

Since the 0.1 cannot get any closer to the exact value of 1/10 and 0.3 cannot get any closer to the exact value of 3/10, then pre-rounding with `round()` function cannot help:

```>>> round(.1, 1) + round(.1, 1) + round(.1, 1) == round(.3, 1)
False
```

Though the numbers cannot be made closer to their intended exact values, the `round()` function can be useful for post-rounding so that results with inexact values become comparable to one another:

```>>> round(.1 + .1 + .1, 10) == round(.3, 10)
True
```

Binary floating-point arithmetic holds many surprises like this.

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