[ale] [OT] Help with Significant Figures Explaination

[Jim Kinney]

A simple explanation of significant figures is:

Given the scale of the measurement, how accurate is the fractional part?

If the measuring scale is meters is it really possible to
measure .0001m? 

The definition I was taught and still use is the least significant digit
is 1/2 the smallest MARKED unit on the measuring device. So a meter
stick marked to the millimeter is good to .5mm. By eye, a reasonable
person can decide if something is closer to 1mm or 2mm but judging
beyond that is too imprecise.

Now add in the error. And accumulate the sig fig work and recall that
the result of a calculation will have no more significant digits the
least accurate measurement. The error grows during calculations. It add
during addition and subtraction and multiplies during multiplications
and division. It never gets smaller. It only gets larger!

Thus is it possible to have a result that is of no consequence because
it is on the same scale and smaller than the error.  This is a large
factor is good experimental design: how to make measurements to lower
the impact of error accumulation.

On Thu, 2008-10-16 at 16:52 -0400, tom wrote:
> OK.  __WAY__ off topic for here, but there are bright souls around who 
> have the training and background that they might have a clue and or an 
> answer.
> 
> Background. I got a gig teaching chemistry at a neaby community college. 
> One of the students asked the always popular "Why?" question this time 
> regarding significant figures. Now one of my books thirty plus years ago 
> had a nice, high school level justification for the rules of significant 
> figures, showing that the rules mostly conserved the relative amounts of 
> error from the raw data to the end result. Of course, I can not find that 
> book right now. Nor am I finding anything on the web.
> 
> Well, that last crack isn't quite true. I have found one site which gives 
> some justification of significant figures using standard deviation and 
> replications. My students aren't quite ready for that level of work. I 
> need something a tad bit simpler, preferably with demonstrations. I would 
> also enjoy showing the limitations of significant figures assuming I can 
> find a nice simple justification.
> 
> My thanks in advance.
> 
> Back to Google et all to try a different approach
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