Re: Sig Figures

[Leigh Palmer <palmer@SFU.CA>]

> With great trepidation I contradict Leigh.
> OK my triple-layered Kevlar body armor is on.  :-)
>
> Errors should be added in "quadrature" i.e. as the square root
> of the sum of the squares. Leigh's method over estimates
> the total error because both (all) of the errors are unlikely to
> be at their biggest (or smallest) extremes simultaneously.
>
> Incidentally I'm SURE Leigh knows this.

Yup, I do, but one might have an answer that depends upon a single
datum. For example, suppose the datum in question was 9. Implicit
precision is that the number lies between 8.5 and 9.5. Suppose
the angle sought is the arctangent of the datum.

                  arctan 9.5 = 83.99 degrees
                  arctan 8.5 = 83.29 degrees

How many "significant figures" are there in the datum? Answer: one.

Clearly a one significant digit angle (8 x 10^1 degrees) is absurd.
The angle is determined to two or three significant figures at the
whim of the unsophisticated teacher. While I would not say that the
angle was so constrained, I would claim that the third digit is
significant here, but I might quote my result as 83.64(35) under
some circumstances, and everyone would agree that the fourth digit
is insignificant.

The significant digit "rules" fail so often that they ought never
appear in a physics course lest students think they are part of
physics; they certainly are not. The business of excess precision
is more easily tackled logically in this day of cheap, ubiquitous
hand calculators. "Significant figure rules" deserve to be junked.

Leigh