Re: [Phys-l] Significant figures -- again

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

If I understand John correctly, he isn't saying that uncertainty should
not be discussed.  Rather, he is saying that such discussion should not
be relegated to a sig figs rule.  He also isn't saying that we need to
replace sig figs with an advanced statistical analysis.  A simple
discussion of uncertainty would do.

For example, I've given students problems like the following: what is
the mass of a cylinder of water, 5.0 cm in height and 1.0 cm^2 in area,
where the density of water is 1.0 g/cm^2.

Many students simply multiply the height and area to get the volume (5.0
cm^3) and then multiply by the density to get 5.0 g.  I always have some
students, though, that first calculate the radius (using pi*r^2) to get
0.56419 cm, which they then round to 0.56 cm.  They then plug that
number into pi*r^2*h to get a volume of 4.926017, which they then
multiply by 1 g/cm^2 to get a mass of 4.926017 g.   Some will leave it
4.926017 g because they know I don't ask them to pay attention to sig
figs, while others will round to 4.9 g (according to sig fig rules).

These students have all learned the sig fig method in other classes.
The problem isn't with their knowledge of sig figs.  It is a problem
with rounding intermediate steps and not realizing the impact of such
rounding on calculations.  Whether they round the end result or not is a
secondary problem.

Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@esu.edu    http://www.esu.edu/~bbq 


-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu
[mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf Of John
Denker
Sent: Tuesday, March 13, 2012 3:00 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Significant figures -- again

On 03/13/2012 11:40 AM, Richard Tarara wrote:
>  Again, as always, the depth and precision of one's teaching depends 
> heavily on the audience and the course goals.  Preparing future 
> physicists is different than preparing future artists, bankers, and 
> the like.

I agree with those generalities ... but I don't think they are on point.

Bankers actually understand the concept of /significance/ ...
they call it "materiality".  They know it is different from precision,
and they absolutely do *not* use anything resembling sig-figs rules for
calculating it.

As for artists and poets, do the experiment sometime.  I have.
When I ask a practicing artist if they learned about sig figs in high
school, they usually say something like "Yeah, I remember something
about that, but it never made any sense to me."

To which I reply:  "There's a reason why it never made any sense to you.
That's because it doesn't make any sense."

1) As I have said before, if the class is not ready for any real
appreciation of uncertainty, don't teach them sig figs.  Just tell them
to round everything off to 3 decimal places (in scientific notation) and
leave it at that.  (Worrying about the uncertainty can come later, if at
all.)

Surely there are already not enough hours in your day, and not enough
minutes in each hour of class.  Surely the time spent on sig figs could
be better spent on something that actually makes sense ... something
that will not have to be unlearned later.

2) For that matter, if/when your class *is* ready for a real
appreciation of uncertainty, once again you should not teach them sig
figs.  Other methods are easier and in every way better.
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