You kind of got me thinking now. The decimal representation of a number is really a string representation (in the sense of a certain sequence of characters). Hence rounding to a certain decimal is essentially a string operation. You can of course do it by (say) dividing by 10^whatever or something else in some numerical fashion, but the more I think about it, the more natural it is to just think of the whole thing as a string.
Or you could flip it around and consider that the string manipulation can also be described numerically so whether you consider the operation as a string operation or a numerical operation is sort irrelevant. It's just a point of view.
It is incorrect to speak of "the" decimal representation of a number, as many numbers have non-unique decimal representations, the most famous example being 1.000...=0.999...
That's true and I'll concede that point, but it's not really relevant to what I said. That just means some numbers have different string representations that represent the same object. That doesn't really contradict anything in my post except the use of the definite article.