What does it mean that uncertainty can be calculated by the "smallest division on a scale"? I have been reading everywhere a little bit to understand the concept of uncertainty but I cannot understand exactly how to find the uncertainty value. On this explanation it says that the uncertainty can be calculated by the "smallest division on a scale". What does this exactly mean?
Thanks.
 A: The smallest possible division on a scale will allow you to establish the uncertainty in a measurement. If you are using a ruler or voltmeter etc., then the maximum error you get when you read off a measurement will be $\pm$ one half of the smallest division.
If for example you are using a ruler, and each of the smallest divisions is one millimeter, and say you measure an object to have a length of $x\ mm$, then you can express your measurement as $$l=(x\pm 0.5)mm$$
So the maximum uncertainty magnitude will always be half the smallest division. Intuitively, this makes sense since if we consider the above example again, you are guaranteed to have the correct answer anywhere between $l=(x-0.5)mm$ and $l=(x+0.5)mm$.
A: It might be easier to appreciate if you imagine using digital devices, such as weighing scales. Imagine you had one in your kitchen that displayed weight to the nearest gram, and another industrial scale, for measuring the weight of lorries say, that displayed weight to the nearest kilogram. Clearly the absolute uncertainty of weights on the first scale seems smaller than the absolute uncertainty of weights on the second scale.
In each case, the scale is rounding the measurement to the nearest whole unit. An apple shown as weighing 233 grams on your kitchen scale could really have a weight anywhere between 232.5 and 233.5 grams, so there is an uncertainty of a gram.
That said, it all depends on an assumption that both scales are equally well calibrated. If your kitchen scale has a fault that randomly adds kilograms to every measurement, then the industrial scale will give you a lower uncertainty for the weight of your apple!
