I recently applied to a PhD program, now accepted and planning to attend, in my CV I entered my GPA as 3.8 although the true value is 3.78.
Will that be a problem when I send the hardcopy transcripts to school?
As pointed out in the comments, you didn't lie. Your actual GPA was a 3.8. By contrast, it'd have been a lie if you claimed a 3.80.
I suspect that reviewers who see this may have one of three reactions:
No concern. They'll see this as entirely correct rounding and not bother thinking about it any further.
Concern about fudging. They'll wonder why you chose to report your GPA on your CV to just 1 decimal place, as this is a bit atypical, and coupled with the fact that it resulted in a round-up, it may come off as a bit of fudging.
Think it dishonest. Committees in STEM fields should really understand that a 3.78 is a 3.8; that's basic numeric literacy. However, if you're applying to a field that doesn't use math, they may perceive it as dishonest.
Personally, if I read a 3.8, I'd have taken it as implying anything from a 3.75 to a 3.84999..., such that the revelation of a 3.78 would be entirely expected. I'd have found your decision to report only 1 decimal place to be dubious, but I'd have already judged you for that upon seeing your CV. Seeing the transcript confirm that the GPA was on the lower end of the spectrum would strengthen the suspicion of intentionally trying to fudge the numbers, but since I'd already have been suspicious of that, it wouldn't really change much.
It depends on why the GPA on your CV reads "3.8" as opposed to "3.78".
If the committee decides the discrepancy is due to you willfully "puffing up" your resume, then they would be justified in rescinding your offer of admission. If, instead, you simply missed the "7" key on the keyboard while entering it and didn't catch it while proofreading, you might be able to convince them of your honesty by proactively pointing out the issue and asking for forgiveness. Even if they believe you, they might still decide to rescind the offer because you have a responsibility to ensure that everything on your CV is accurate.
On the other hand, they might not see that 0.02 difference as qualitatively different, and maybe they'll overlook it. But at the very least, it will leave a bad taste in their mouths. You would not be well-served by letting them discover that issue on their own.