This isn't super complicated. I have a GPA of 2.997 (we'll put aside whether that's good enough to get into grad schools). Why my institution gets so specific is a mystery to me. I report it as 3.0/4.0 on my resume because I don't want to be a victim of the psychological 99¢ effect, and because it's an honest rounding when you report to one decimal place as most people appear to.
In applying to grad schools, I've circulated my resume to recommenders (who don't always request transcripts) and obviously my graduate schools are going to get my transcripts and my resume--so I don't feel like this rounding lacks integrity. They will get all of that information and then some. Still, I want to make sure I'm not losing any sleep over it. If people here think it sounds fishy then I'm sending an email to all my recommenders making sure they understand what I mean by 3.0/4.0. Otherwise I'm going to stop obsessing about it internally. But it's been bugging me because one of my recommenders told me he plans to rate me 5/5 on integrity and I don't want to make him a liar on that. I don't mind sinking or swimming on 2.997.