daniel added a comment.

@Jc3s5h Hm... it doesn't seem to be that clear cut. A quick search brought up a 
somewhat inconclusive picture:

Frontiers of Science: Scientific Habits of Mind 
<http://ccnmtl.columbia.edu/projects/mmt/frontiers/web/chapter_5/6665.html> 
(Columbia University) seems to agree with you:

> 6. Trailing zeros in a whole number with no decimal shown are NOT 
> significant. Writing just "540" indicates that the zero is NOT significant, 
> and there are only TWO significant figures in this value.


Wikipedia 
<https://en.wikipedia.org/wiki/Significant_figures#Identifying_significant_figures>
 (referencing Higham, Nicholas (2002). Accuracy and Stability of Numerical 
Algorithms (2nd ed.). SIAM. p. 3.  and Myers, R. Thomas; Oldham, Keith B.; 
Tocci, Salvatore (2000). Chemistry) however sais:

> The significance of trailing zeros in a number not containing a decimal point 
> can be ambiguous. For example, it may not always be clear if a number like 
> 1300 is precise to the nearest unit (and just happens coincidentally to be an 
> exact multiple of a hundred) or if it is only shown to the nearest hundred 
> due to rounding or uncertainty.


The ChemTeam Tutorial for High School Chemistry 
<http://www.chemteam.info/SigFigs/SigFigRules.html> puts it this way:

> How will you know how many significant figures are in a number like 200? In a 
> problem like below, divorced of all scientific context, you will be told. If 
> you were doing an experiment, the context of the experiment and its measuring 
> devices would tell you how many significant figures to report to people who 
> read the report of your work.


In other words: context is needed.

In practice, assuming that 3000 has just 1 significant digit is going to be 
right in 90% of the cases (exactly 90%: the chance that the last digit is 0 by 
accident is 1:9). 90% sounds pretty good, but it's going to be wrong thousands 
of times per day. Erring on the side of caution will more often be wrong, but 
will not lead to loss of (displayed) information.

I'm not sure what would be best. Since this kind of "guessing" only occurs 
during interactive input, we could improve the interaction to avoid mistakes. 
For example, when the user enters trailing zeros, we could show a popup asking 
them to tell us the number of significant digits; we could also gray out any 
insignificant digits in a preview/feedback display. This needs more thought, 
and probably a separate ticket.

This ticket is about deciding whether the magnitude of the default uncertainty 
should be halved. And I'm increasingly convinced that it should. Not 
surprising, since that was my initial intuition. But I want  to be really sure 
before making a change like this. Being forced to change it again later would 
be awkward.


TASK DETAIL
  https://phabricator.wikimedia.org/T105623

EMAIL PREFERENCES
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To: daniel
Cc: Jc3s5h, thiemowmde, kaldari, daniel, Stryn, Lydia_Pintscher, 
Liuxinyu970226, Snipre, Event, Ash_Crow, mgrabovsky, Micru, Denny, He7d3r, 
Bene, Wikidata-bugs, Ricordisamoa, Kelson, MSGJ, Klortho, Wolfvoll, Aklapper, 
aude



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