[Phys-L] Re: infinite sig. figs.

[John Denker <jsd@AV8N.COM>]

Edmiston, Mike wrote:

> The question is, will people generally recognize what
> three-digit-representation means?
>
> I hope it does not mean the same thing as another set of words John
> used... "three decimal places."

How about this:
  -- three digits of scientific notation.

Other things to consider include:
  -- In math or computer class I would call it floating point with three
digits of mantissa.

=============

Also, in my previous note, I hope people didn't think that I meant
that 3 digits was equivalent to 0.1% resolution.

In fact, three digits is barely enough to ensure 1% resolution, and
barely enough to keep the roundoff errors below 1%;  for example
consider 0.101 versus 0.102.

This is interesting, because percentage resolution is what matters
conceptually, but counting the digits is where the rubber meets the
road operationally.

The point is (as always):  Please do not try to encode the significance,
or the uncertainty, or anything else in the digit-count.
   *) Given the required resolution, or the required roundoff-error budget,
    you can figure out a _lower bound_ on the number of digits required.
   *) Given the actual number of digits, you *cannot* infer the significance,
    nor the uncertainty, nor anything else ... neither an upper bound nor a
    lower bound.  Canonical example:  suppose you see the number 2.54 in the
    window of the calculator.  By itself it tells you _nothing_ about its
    significance or its uncertainty.
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