[cauch]

I still don't get it.

You are explaining error propagation, but my point is that _if you are doing error propagation (as you should do if you want to do things properly), significant figures ARE just for making deliverable pretty_.

You are talking about measurement uncertainty. Measurement uncertainty is written x +- y, with y being the uncertainty.

If you don't do that and use significant digit instead, you lose the information and precision: 10.0 +- 0.1 is 10.0, 10.0 +- 0.2 is 10.0, 10.0 +- 0.3 is 10.0, ...

This is why the other person was talking about "arbitrarily rounding".

You should _never_ said "well, it's a measurement of 10.0 with a 0.2 precision, so I can write 10.0", you should _always_ write 10.0 +- 0.2 (in which case, you can also write 10 +- 0.2 or 10.000 +- 0.2, the significant digits have no impact on any future results). Writing 10.0 instead of 10.0 +- 0.2 is just a terrible practice that does not have much justification, 10 +- 0.2 is always a better way. (and my point is that the problem you have with the significant number disappear if you teach people to use a non-clumsy way)

(and, no, you should not do the distinction "it's a measurement, so it's written differently", because in practice, a lot of "measurements" are in fact already a transformation, and sometimes you cannot even know for sure yourself. For example, a temperature sensor will measure an electrical resistance (with a measurement uncertainty) and then convert it into a temperature, and according to you, it should not be written the same way, just for arbitrary reasons)

[nicklecompte]

I don't think you understand what a measurement is. There's a very good, very short book that explains in more detail what I am talking about, in the context of physics experiments: https://www.amazon.com/Practical-Guide-Data-Analysis/dp/0521...

[cauch]

I think your notions are just too basic. It's a bit like in school when the teacher says "you should write all your sentences as subject + verb + complement". It is good at school, to teach students the basics and to put boundaries of the studied regions (you don't want to have students using more complex notions by accident and having to cover everything in lesson one), but as soon as you begin to be a professional writer, you realise it is better to ignore this rule.

I know the notion of measurement that you try to explain, I've studied it when I was an undergraduate students. Since then, I have passed beyond this notion and use something better. It's not a matter of "you don't understand", it's rather a matter of "you understand too well and see the limits of this notion and that it's not useful for you anymore".

The book you share seems to confirm that: it is for undergraduates. Things get more complicated with real world practice, and the basic rules used to forge the understanding needs to be left behind. For undergraduate students, they are going to do basic lab experiment with a ruler and a chronometer, and the goal is just to practice, not to answer to a real unknown situation. In real life, no one needs to measure things as trivial as what they are measuring. When people do that, they realise that the distinction between calculated value and measured value is meaningless and not helpful at all.

Again, as I've said, you just use x +- y and you don't have any problem. What would be the problem of using x +- y that you will not have otherwise (knowing. of course, that you are educated enough to understand very complex notion and that therefore you totally understand and know things as trivial as significant digit already)?