[ale] [OT] Help with Significant Figures Explaination

[Greg Freemyer]

I think it is relatively easy to explain via an experiment / lab:

You have a random stack of paper about 6 centimeters tall (2 1/2
inches).  Have lab partner 1 measure it with a standard ruler that can
do millimeters.

Say it is 63mm tall.

Now have lab partner 1 take a single piece of paper.  Measure its
thickness with a micrometer or some other more accurate tool.  I'll
guess it is about .1mm.

(If you don't have a fine grained measurement tool, measure the height
of a stack of exactly 100 sheets and divide the measurement by 100 to
get each sheets thickness.  That also shows significant digits
relative to division.)

Add the single sheet to the stack and have lab partner 2 measure the
stack and write down the thinkness on a piece of paper and turn the
paper upside down.  (Hint: It will still measure 63mm.)

Now have lap partner 1 guess what is written down on lab partner 2's
piece of paper.

The odds are very high that the two disagree.

Now have them repeat the process, but have them follow rules about
rounding and significant digits.  Hopefully they can agree on how tall
the stack is.

===> Now for multiplication

Repeat the above, but now add 37 sheets of paper to the stack not one.
 (But don't measure the height of the 37 sheets, just of one sheet.)

Does that help.

Greg

On Fri, Oct 17, 2008 at 11:33 AM, Thompson Freeman
<tfreeman at intel.digichem.net> wrote:
> To start, thanks to both you and Robert for responses.
>
> As an aside, I had a friend in the banking business of the
> early 1990's who reported something similar to your
> accountant charge. He sat down with his opposite number in
> another trust division one day, and some eight hours later
> they still could not reconcile their common "numbers"
> closer than hundreds of millions of dollars. Admittedly the
> story is hearsay, so take it for what it is worth.
>
> To the main topic of tonight's symposium... (with
> appologies to Tom Leher)
>
> I've gotten students to accept the need for, and to
> (largely) use significant figures. This isn't the challenge
> any more, thankfully.
>
> They have a challenge justifying the two computational
> rules, as in "Why does this work this way?" Dumb these
> students are not. Just not sophisticated enough to tromp
> through a statistically oriented exposition (which I would
> need time to relearn myself). Hence my interest in a less
> sophisticated development of why significant figures
> calculations work the way they do.
>
> Example time: 752 x 1256 = 944512 in arithmetic, or 944000
> when _reporting_ the result in a lab exercise. The reported
> value is rounded to have the same number of sigfig as the
> smallest number of sigfigs in the multiplicands.
>
> The other piece, which everybody remembers, is addition.
> 23.45 - 19.4578 = 3.9922 as pure arithmetic, but 3.99 when
> reporting the results computation from data. For addition,
> you ignore all the digits to the right of the larger least
> significant digit.
>
> Of course, the point of both rules and the determination of
> significant figures in the first place is to indicate the
> level of uncertainty without explicitly calculating and
> displaying it. Many of the items I have located on the web
> are suggesting that we should completely ditch significant
> figures and routinely compute the statistical uncertainty -
> a noble goal but not happening in the near term.
>
>
>
> On 10/17/2008 08:32:28 AM, Jeff Lightner wrote:
>> You might talk about how "significant" the figures become
>> in space.
>> What appears to be "insignificant" at the start of a
>> launch to send
>> something to Jupiter for example becomes greatly
>> "significant" in error
>> by the end of the trip due to magnification over distance.
>>   It would be
>> embarrassing to set your multi-billion dollar satellite to
>> do a drive by
>> on Jupiter only to see it instead miss it by nearly as
>> many miles as the
>> dollars that were spent.
>>
>> Also "significant" in numbers doesn't always have to be
>> that far right
>> of the decimal.  Most accountants spend more time worrying
>> about why
>> they're off a penny (0.01 dollars) than why they're off
>> $3,000,000.00
>> simply because it usually a lot harder to find that penny.
>>  Why worry
>> about a penny?  Because if you're off a penny it indicates
>> there is an
>> error and you have no way of knowing whether the error is
>> just a penny
>> one way or if it is instead a variance of $3,000,000.00
>> one way and
>> $3,000,000.01 the other way.
>>
>> -----Original Message-----
>> From: ale-bounces at ale.org [mailto:ale-bounces at ale.org] On
>> Behalf Of
>> Robert Reese~
>> Sent: Friday, October 17, 2008 12:07 AM
>> To: ale at ale.org
>> Subject: Re: [ale] [OT] Help with Significant Figures
>> Explaination
>>
>> Why not contrast them to "insignificant figures"?
>> Sometimes teaching
>> the opposite works just as well, or even better, than
>> teaching the
>> topic.
>>
>> Cheers,
>> Robert~
>>
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