Even though accelerometer is sitting still, numbers jump around?

Yes, I think so - how much do they fluctuate by? Have a look at the chip's datasheet - it should have some numbers.

As soon as you start doing stuff with the real world, absolutely everything you read has a percentage error. Often a device will give you more bits of data than it is actually accurate to - because over time you could do some filtering on those values and you might just squeeze a little more out of it.