Re: Significant figures - a Modest Proposal

[Robert A Cohen <bbq@ESU.EDU>]

On Thu, 26 Aug 1999, Glenn Knapp wrote:

> [snip]
>
> I teach high school physics and chemistry and physics for the local community
> college.  The first chemistry meeting we were reviewing powers of ten and
> scientific notation -- I hadn't gotten to significant figures yet.  One of the
> students who had been in my high school physics class two years earlier was
> very uncomfortable with the work  --  "What  about significant figures!"  She
> was used to doing them and did not like to see a bunch of arbitrary digits that
> weren't justified (at least to her thinking) up there on the chalk board.
>
> I can't debate the absolute relevance of significant figures -- whether in fact
> the rules do all that they are supposed to do -- but they are pretty standard
> in most texts in both chemistry and physics.
>
> I think they are worth doing.

I am going to try out a new activity this semester in my algebra-based
physics course (undergrad).  I am providing each student with the
nutrition label off of a food product.  The label lists the amount of
sodium in the product and the corresponding "percent of the daily value".
I then ask them to calculate the daily value from this information.

The daily value is listed on the label as 2400 mg but students will not
get that value (even when rounded to two digits).  I am hoping that the
wide variation in calculated values will spur some thought.  In addition,
some will get a number like 2567 (which rounds to 3000 or 2600, depending
on the number of significant figures) and I'm hoping they will realize the
need for a better method than significant figures.

By the way, I also teach a course for students who are a semester or two
from student teaching in high school science.  By and large, they think
that significant figures is *the* way, as if there is something magical
about it. They are surprised to learn that it is a rather poor way of
doing things (but much better than nothing!).

While I'm on the topic, I should mention that I will be emphasizing the
distinction between precision and resolution and that both contribute to
the accuracy of the measurement (I haven't done so in the past).  The
activity above is designed to introduce the idea of resolution and its
effect on calculations.  The second activity is designed to introduce the
idea of precision and its effect on calculations (they time cars and see
how many are speeding - the timer provides measurements to the hundreths
of a second but the precision is not that good).  If anyone has any
experience with teaching this, I'd appreciate pointers.

P.S. A year or so ago, there was an article in The Science Teacher about
measurement.  It turns out that many students do not know how many digits
to include in a standard measurement (e.g., with a ruler).  Unfortunately,
the task was worded poorly (i.e., determine the length of this object
within the accuracy of the meter stick).  I'd argue that a typical meter
stick can be read down to a few tenths of its smallest resolution but that
a typical meter stick is not as accurate as that (due to possible warping,
parallax, etc.).

----------------------------------------------------------
| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
----------------------------------------------------------