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[Phys-l] sig figs

Suppose you are given a value and you have reason to believe that the
provider of the value used significant figures conventions in deciding
how many significant figures to write in the value. Significant figures
represent a vague way of providing the uncertainty in the value while at
the same time giving the mean value of the corresponding distribution.
The reader and the writer are both supposed to understand that the value
is given up to and including the first digit that is uncertain. So,
when someone writes that g = 9.80 m/s^2, they mean that the last digit
is uncertain. The writer is not telling you how uncertain the digit is,
just that it is uncertain. (I got this information from the
introductory calculus-based physics course taught by Dr. Harry Meiners
at RPI during the 1978-1979 academic year. Dr. Larry Schecter and Dr.
Kenneth Krane said the same thing in a video shown to students during
the Oregon State University first laboratory session in the laboratory
component of the algebra-based and/or calculus-based introductory
physics course circa 1983. I am going by memory here-apologies to all 3
if I have it wrong. The scheme falls apart when the author gives a
value with only 1 sig fig, in which case, unless context clues dictate
otherwise, I take the value to be an order of magnitude estimate.) The
value g = 9.80 m/s^2 with sig fig conventions represents a distribution
that is among the distributions 9.80(1) m/s^2 to about 9.80(9) m/s^2.
The sample of gravitational acceleration values for each of 44 world
cities given on page 57 of the instruction manual
http://www.andweighing.com/and.nsf/html/WEBB6853UH/$FILE/HC-i_IM.pdf
for the A&D HCI series of counting scales has a mean and standard
deviation (of the values in the sample from the mean using n-1 degrees
of freedom) of
(9.800 +/- .011)m/s^2
This is consistent with the global average value
9.797645 m/s^2 quoted in Wikpedia (without any indication that I see, of
the source of the value or the standard deviation or standard error).

If a textbook author quotes the value as 9.8 m/s^2, either the author
has chosen not to adhere to significant figures convention or the
narrowest distribution the author is communicating to the reader is
about
(9.8 +/- .1)m/s^2
I think that this standard deviation (.1 m/s^2) characterizes a broader
distribution than the actual distribution of world values so I assume
the author has chosen not to adhere to significant figures convention
and that is okay by me.

I can think of good reasons why a teacher or author would choose to use
9.8 m/s^2 or 10 m/s^2. I think that the value 9.81 m/s^2 used by the
state of NY is reasonable-the mean differs from the average value
representative of the populated parts of the world by "1" in the
uncertain place and I think the range of standard deviations implied by
the value encompasses the actual standard deviation of the values from
the mean. It has the advantage of being consistent with the standard
gravity value defined for commerce purposes to be 9.80665 m/s^2. In
other words, the state of New York has chosen a value that differs from
the mean global value by an amount that is "in the noise" and one that
vaguely communicates a standard deviation that is consistent with the
actual standard deviation of the world values from the mean. I prefer
9.80 m/s^2 but when using a book in which the author uses one of the
other values mentioned here, I go along with the author.



-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Herb Gottlieb
Sent: Sunday, November 19, 2006 11:00 PM
To: phys-l@carnot.physics.buffalo.edu
Cc: phys-l@carnot.physics.buffalo.edu
Subject: Re: [Phys-l] g...

What, if anything, will happen if you do not conform , and use a
correct
value for the acceleration of gravity in your course and while grading
the students'
regents examination in June?


On Sun, 19 Nov 2006 22:18:03 -0500 "R. McDermott" <rmcder@gmail.com>
writes:

----- Original Message -----
From: "Herb Gottlieb" <herbgottlieb@juno.com>
To: <phys-l@carnot.physics.buffalo.edu>
Cc: <phys-l@carnot.physics.buffalo.edu>
Sent: Sunday, November 19, 2006 8:58 AM
Subject: Re: [Phys-l] g...



On Sun, 19 Nov 2006 08:13:29 -0500 "R. McDermott"
<rmcder@gmail.com>
writes:
I introduce g as the strength of a gravitational field due to
the Earth, remind them that it varies with distance, etc, and
has
a value of 9.81 N/kg at the Earth's
surface.

If you wrote that g has a value of 9.8 N/kg at the Earth's
surface, I would agree. But is it correct to add the additional
significant figure and make it 9.81 here??

NY State syllabus (and reference table) now gives it as 9.81, not
9.8 as in previous years. We are obliged to conform.

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l