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Re: [Phys-l] Sig figs

On 10/13/2010 11:18 AM, Josh Gates wrote:

I had to come here, because my chemistry colleague is a sig figs
devotee. He has done quite a bit of "real chemistry," and tells me
that he uses sig figs in work for publication - does anyone know if
that's the standard expectation in chemistry journals, or is it just
not important, if you're publishing a characterization of some
previously-undescribed plant aroma molecule or describing a new
synthesis process for something?

That raises a number of issues.

1) Sig figs are a convenient way of getting the wrong answer. For
details, including suggestions on how to do things right, see

2) I assume this discussion revolves around the sig figs rules such
as one finds in introductory chemistry texts.

Having said that, we should keep in mind that some people use "sig
figs" as an idiomatic expression to refer to the broad topic of
uncertainty, even though they would never take the sig figs rules

3) The American Chemical Society publishes dozens of journals, each
of which has its own policy.

3a) As for the flagship journal, /JACS/ does not require the use of
sig figs. In fact, neither the instructions to authors nor the
instructions to reviewers say anything about uncertainty, accuracy,
precision, standard deviation, or significant figures, so far as
I can tell by searching the following documents:

3b) ACS /Medicinal Chemistry Letters/ expects authors to be "cognizant
of significant figures" whatever that means ... but they also leave
the door open to explicit statements of "error limits" such as
standard deviation.

3c) I have not checked all the ACS publications, but I tend to
doubt that any of them have a strict policy concerning sig figs.

3d) The bad news is that the ACS /J Chem Educ/ is infested with
an endless stream of articles on how to "explain" sig figs to

In the other pan of the balance, there are occasional articles
that point out the absurdity of sig figs, e.g.
H. Bradford Thompson, "Is 8°C equal to 50°F?"
J. Chem. Educ. 68, 400 (1991).

4) Moving outside the ACS, it is not hard to find chemistry-related
journals that blatantly call for the use of significant figures,
such as Wiley's /Environmental Toxicology & Chemistry/
However, I do not think this is the norm.


No matter how you interpret the instructions, the fact is that I have
seen things like "18 ± 12" in the chemistry literature, i.e. things
that for good reason dramatically violate the so-called sig figs

The important point is this: No matter what the instructions say,
if you write something that violates the sig figs rules, such as
quoting the NIST value of e = 1.602176487(40) coulomb, no sane
reviewer is going to complain. And I daresay if you find a journal
that actually enforces sig figs rules, you don't want publish in
that journal. Resubmit elsewhere.


The primary, fundamental, and overarching goal of every course
(and of the education system as a whole) should be to help the
students improve their critical thinking skills.

High-school students have plenty of ability when it comes to
imagination, abstraction, formalism, et cetera. You can see
it in the games they play outside of class. However ... many
of these same students systematically fail to demonstrate such
skills in the classroom.

It is easy to see where this comes from. They have been taught,
year after year, that conformity and rote regurgitation pay off,
whereas actually thinking about the material just gets them into
trouble. This is the entirely foreseeable result of year after
year of being taught things that cannot possibly be true.

When the chemistry books spends the first one or two chapters
focusing on things that don't make sense, it puts students on
notice that they should just shut up and rote-memorize the
material, and that thinking will not be tolerated in this
course. The pattern that is laid down in the first chapter
continues throughout the book. I'm talking about things like
-- chemical vs. physical change
(based on qualitative macroscopic observations)
-- sig figs
-- the cut-and-dried five-step "scientific method"
-- filled "Lewis octets" in molecules
-- entropy = disorder
-- et cetera.

Some of the widely-used physics books are comparably bad. See

So ... let's be clear: It's worth making a fuss about the sig
figs rules for two reasons, one small and one big. We should
not let the small reason obscure the big reason:
-- The topic of uncertainty has some modest direct importance.
-- Sig figs have a huge indirect importance. They are the
dead canary in the coal mine. They are symptomatic of an
appalling lack of critical thinking.