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Re: Sig Figures

I'm a little late getting into this but I have a few questions...

On Tue, 1 Feb 2000, John Denker wrote:

[snip]
running_totals
item thickness Moe Joe
1 0.03 0.03 0.03 (all measurements in cm)
2 0.04 0.07 0.07
3 0.03 0.10 0.10
[snip]
27 0.04 0.92 0.92
28 0.03 0.95 0.95
29 0.03 0.98 0.98
30 0.04 1.0 1.02
31 0.04 1.0 1.06
32 0.03 1.0 1.09
[snip]

Wouldn't the rules of sig figs say that 0.98 + 0.04 = 1.02? Why would
addition imply that the answer must be rounded to two sig figs?

Also...

On Tue, 1 Feb 2000, Richard Bowman wrote:

[snip]
5. IMHO, never round off intermediate results.
[snip]

Suppose we have an object traveling at a constant speed of 6.24000 m/s.
After 0.200000 seconds, the object has traveled 1.24800 m.

Now suppose that we measure the distance to 3 sig figs, i.e., 1.25 m, and
want to calculate the acceleration of the object (which should be zero).
I use

a = (2/t^2) * (x - vt)

When I don't round to the end, I get an (incorrect) acceleration of 0.100
(3 sig figs). If I round at each step, then I get a (correct)
acceleration of 0. The difference comes during the calculation of (x-vt):

(1.25) - (6.24000)* (0.200000) = 1.25 - 1.248

This equals 0.002 if not rounded or 0.00 if rounded. Doesn't this mean
that I should round the intermediate results?

P.S. FWIW, I emphasize in my class that sig fig's is the "rough" way of
estimating the effect of resolution on a calculation and it is better than
nothing but that there are "better" ways.

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