Re: [Phys-l] formatting uncertainties

[John Denker <jsd@av8n.com>]

On 01/23/2008 11:09 AM, Rick Tarara wrote:
>  Having 4 'guard' digits in the 
> answer seems more confusing to me--does the student really understand the 
> level of uncertainty in the answer?

a) Of course they don't understand it.

b) If you take away the four guard digits, they still don't understand it.

Combining (a) and (b), this seems like a vanishingly weak
argument against the guard digits.

The only way I can make sense of this situation is in the case
where the cure is worse than the original disease.  That is,
if you round off sufficiently brutally that roundoff error is 
the dominant source of uncertainty, then you know what the
uncertainty is.  But why would you want to do that?  Designing
an experiment or a calculation such that roundoff error is the 
dominant source of uncertainty is the hallmark of bad design.  
Why should we tempt (let alone require) students to go down 
that rabbit-hole?