[ale] [OT] Help with Significant Figures Explaination

[Thompson Freeman]

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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