There's less and less reason to do it (and it's never 5). On systems without floating point you might want to do round it a bit, but only if the specific thing you're doing allows it, and even then you're more likely to do a fixed-point approach by using e.g. 314 and dividing by 100 later, or adjusting that value a bit so you can divide by 128 via bitshift if you're on a chip where division is expensive. However, in 2025 you almost certainly should have picked a chip with an FPU if you're doing trigonometry.

And while rounding pi to 3 or 4 is certainly just a meme, there are other approximations which are used, like small-angle approximations, where things like sin(x) can be simplified to just x for a sufficiently small x.