There is a difference between uncertainty and error. Uncertainty is the maximum possible or maximum likely error. Error, is the actual error in the measurement.
In your meter stick example, the uncertainty is a matter of confidence in your measurement. Some will claim you can only measure to 1mm because that is the smallest increment on the device. In actuality, normal practice is to go one level lower, that is, it is normally considered you can accurately estimate one level more than the meter stick shows, so you can measure to the nearest tenth of a millimeter. Often to acknowledge this last digit was an estimate, you would then say the uncertainty was +/- 0.3mm rather than +/- 0.1mm. With any digital device you do not have this ability to extrapolate one more level, so you must take the reading directly from the device, then know the inherent uncertainty of the device. Just because a digital stop watch for instance gives a reading to .001 seconds, the device may actually count 0.003 at a time giving an uncertainty in the reading higher than the least significant digit. Those numbers though are the uncertainty in the device, the the actual error of the readings.
To actually calculate what the error is though, you go to a statistical analysis of the data, such as a mean and standard deviation. 840
As an example, say you had 100 people measure the same object with the same meter stick. The uncertainty of the meter stick is the same for each, say you accept the +/- 0.3mm I proposed. But they will not all get the same measurement. Some will measure wrong. Some will estimate the last digit differently, etc. Most should be within that +/- 0.3mm though. You would then get your mean, and standard deviation to get what you considered the real measurement and calculated error in that measurement. Many times, you would also refine that by throwing out any measurements that were more than 0.3mm off from the others as measuring errors, or maybe those more than 2-standard deviations, etc. as you know everyone used the same device and measured the same object so numbers outside of that range are not real. 964