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

I think I run into some of the folks that follow the kind of advice in the message below. By way of a simple example of what this leads to: On using a pan balance marked off to the nearest 10th of a gram, they round off to the nearest gram before they write down their "raw" data. So they have thrown away two digits of information (the reading can be estimated to the nearest hundredth of a gram). They have thrown away the information they need to get a good estimate in the statistical uncertainty in a collection of such measurements. Eventually, sometimes, they have a whole column of data containing the same value in every cell and their statistical analysis of their data shows they have no uncertainty. This even happens, in other kinds of circumstances, with devices that give digital readouts--people round the reading before writing it down.

Significant figures represents a rough way of communicating both a value and the uncertainty in that value. I think everyone uses it. In my opinion, even John Denker is using it when he writes a value like 3.8675309 ± 0.5 cm [which, incidentally, should be written as either 3.8675309 cm ± 0.5 cm or (3.8675309 ± 0.5)cm ]. By writing the uncertainty as 0.5 cm rather than 0.50000 cm, he is telling me that his uncertainty value is itself a rough estimate. Being absolutely consistent in writing a separate value for the uncertainty in every value one writes down would lead to an endless recursion in writing down a single result (with the uncertainty in it, and the uncertainty in its uncertainty, and the uncertainty in the uncertainty in its uncertainty etc.) Significant figures represent a crude way of communicating uncertainty. A guy named Harry Meiners at RPI taught us another crude way of communicating the uncertainty. At the time (my freshman year) I had no idea that it was not the universally-accepted method. With sig. figs. one writes down all the digits up to and including the first one that is just an estimate. Harry Meiners taught us to write down as many more digits as we wanted and put a bar over the first one that was just an estimate (typically but optionally extending the bar over all the digits less significant that that one too). One could have plenty of guard digits while still conveying a crude estimate of the uncertainty. The method eliminates all the bad things about the significant figures method and still allows one to convey a rough estimate of the uncertainty. I don't know why it (or something similar--an underscore is easier to type than an overbar) isn't more widespread.

There was a theoretical nuclear physicist at Oregon state that, in seminar presentations, would present results with about a dozen significant figures even though the uncertainty was probably in the ballpark of .1 to 20 percent. My recollection is that they were photocopies (onto transparencies) of computer printouts. I don't think he was being stupid or rude, he was simply providing values without providing any information in the uncertainty in those values.

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Paul Lulai
Sent: Monday, March 12, 2012 12:27 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Significant figures -- again

I've found that stating in terms of what they can measure or make helps a
bit. When a kid gives me an answer of 3.8675309 cm (or anythings), I ask
them if they could cut a board to that length. It seems that they are less
comfortable making something a certain length (or weight etc...) than they
are measuring to that precision. Meaning if you give a 9th grader (or 12th
grader, and I assume college kid) a board to measure, they are happy to claim
it is 3.8675309 cm long. Asking them to cut a board to that length makes
them think a bit more about what is appropriate.

Paul Lulai
Physics Teacher
St Anthony Village S.H.
3303 33rd Ave NE
St Anthony Village, MN 55418

612-706-1146
plulai@stanthony.k12.mn.us
http://www.stanthony.k12.mn.us/hsscience/