I have always understood significant figures to be those figures which we know with certainty. Wikipedia (https://en.wikipedia.org/wiki/Significant_figures) provides a related but less rigid definition of "[the] digits that carry meaning contributing to its measurement resolution."
To use an example from another post on this topic, suppose a pencil were measured to be somewhere between 86 and 87 millimetres, but closer to 86. I understood that we would round to 86, and the value would be written with its two significant figures. We would then understand that to mean 86 millimetres +/- 0.5 millimetres. This is consistent with our definition because the two figures, 8 and 6, are known with certainty (assuming that our measurement was correct). However, various other posts, including Definition of Significant Figures to which I refer above, provide a slightly different methodology. It proposes that we estimate the next digit (3 in the example), and write the value with three significant figures: 86.3. Recognising that the last figure was an estimation, we take our uncertainty to be +/- 0.1.
The examples above are obviously incompatible. The method that I learnt is consistent with both of the definitions. We do know both figures with certainty, and they carry meaning contributing to their measurement resolution. However, in the example above, it is clear that we have introduced more uncertainty that is probably warranted. Indeed, by recognising that the pencil was between 86 and 87 millimetres, and closer to 86, we can presumably be certain that the real value is between 86 and 86.5, removing half of the uncertainty introduced by the first method. The second method improves upon our understanding of the real value, but it introduces an estimate and proposes it as significant. Consequently, the first definition of significant figures does not apply. Furthermore, it is impossible to make such an estimate with most measurements (with electronic devices, or where the value is not so easily perceptible), and in such cases one would presumably have to revert to the whole number +/- 0.5 of the unit value of the last significant figure.
Both methods, incidentally, collapse when one introduces operations - something I intend to address in another post.
Is there a gold standard as to the method that is used in professional circles? Indeed, are significant figures used in any professional circle at all, and if so, which?
