[JohnGilb]

Some drift may be predictable - you might notice that your gyro has a pretty constant 0.05 degree/second drift in one direction. You could compensate for that in software (and probably should!).

However, as you look closer and closer at the drift, trying to compensate more and more accurately (hmm, looks like it was 0.051, or maybe 0.05102...), you'll eventually hit a point where the drift is no longer predictable - the drift is essentially small and random in both directions.

Essentially, the more expensive / higher quality a gyro you have, the smaller that "noise" value is. Also, operating in ideal conditions (temperature-controlled, constant voltages) will reduce that noise further.

But it won't be totally eliminated, and these errors accumulate.