Where reputation is shown in shortened form it is rounded conventionally. That being;
So my current rep of 11,374 is shown as follows:
This doesn't really matter on desktop as the real rep is shown in the top bar, this isn't the case on mobile however.
Could shortened rep always be truncated (and probably other numbers too, for consistency), so I would be shown as having 11.3k.
Ultimately I didn't care about moving from 9,949 to 9,951, but it looked like a big deal as it showed up as 10k, where I get "access to moderator tools", however when I actually got to 10k nothing changed. This tricked me at almost every rep level (possibly I shouldn't admit that).
Every single privilege sits at exactly divisible powers of 10 (apart from the very first ones) so it makes sense for the shown reputation be rounded such that when the shown reputation matches the required reputation you actually have the privilege.