Might be easier not to round at all, only take the floor. Then you never get to 100% until you're actually at 100%. You never get to 50% until you're actually at 50%.

And then in terms of the 0% vs 1% thing... my preference is to show 0% but keep an animated indicator so you know it's in progress, if you don't have something else that does the same (like showing the current download speed or current frame). Showing 1% done when it's only at 0.0001% done doesn't feel quite right to me.