Dispute over precision with coauthor I am currently having a disagreement with a coauthor on a paper over the matter of significant figures.

He would like to specify (for example) that a certain organization has an environmental footprint of 7,622 gha.  Environmental footprinting rests on a tonne of assumptions and is not a precise methodology, so I don't think we have anything like 4 significant figures of precision in our calculations - more like 2 at most.  So I would like to publish that figure as 7,600 gha.

I have pointed out that doing otherwise implies a level of precision we don't have.  Currently we are publishing an executive summary prior to peer reviewed journal paper, so I also said it would be embarrassing if the precision issues were picked up at peer review stage and we thus ended up publishing two different sets of figures.  He responds that he has never had a problem with publishing more accurate figures in previous journal publications.

The coauthor does not have a quantitative background so has limited understanding this issue, however he is more senior.

So two questions


does this issue even matter?
what would you do about it?


UPDATE

It looks like you all agree with me that this matters.  Good, I'm not insane :)  

As we are currently writing an executive summary/press release for the general public, there is no place for scientific notation or estimates of error - they will make it harder to read and likely put off some people.

Can someone link me to a good, polite and authoritative rant on why this matters that I can show to my colleague?  The trouble with almost all material I have seen on significant figures, is that it doesn't discuss rounding off digits left of the decimal point.  i.e. it talks about turning 7.36654 into 7.4 but not 736654 into 740000.  I suspect my colleague draws an arbitrary line in his head at the decimal point, being unaware that the position of the point is just a function of the units used.  And I doubt they would be open to that sort of argument.
Just because you have the additional digits, doesn't mean you should report them.

Accuracy and precision are extremely important concepts in the reporting of scientific data. Excessive precision, as you suggest, implies too much reliability in the accuracy of scientific data. For instance, someone turned in a report to me saying that a particular parameter was known to be:


  E = 1.3405987423423 GPa


If this were to be published in a paper, it could be rejected out of hand for incompetence, because the parameter E is often known only to one or two decimal places, let alone four. 

In general, you need to make your reporting consistent with the assumptions and the accuracy of the measurement techniques. One way to figure this out is to note the accuracy of your measurement—what is the expected error in the measurement? If the error in your measurement technique is, for instance, plus or minus 1 global hectare, then by all means report it to the nearest hectare. If it's plus or minus 1000, though, reporting to the nearest hectare will look quite silly.

How do you deal with this? (I've actually had to do something like this before. Similar argument, but not exactly the same.) In this particular instance, engaging in a little hyperbole might be useful. Instead of reporting it to four significant digits, show him a version of the text that lists the data to the full precision you have available—something clearly ridiculous that reports things down to six or seven decimal places, if possible. Then, when he argues that what you're doing doesn't make sense, you can argue "what's the harm in reporting extra digits?" That should be enough to have your coauthor "see the light."