Significant figures calculation

[Erik Max Francis]

Steven D'Aprano wrote:
> On Tue, 28 Jun 2011 06:53 am Ethan Furman wrote:
> 
>> Harold wrote:
> [...]
>>>>>> Empirical('1200.').significance
>>> 2
> 
> Well, that's completely wrong. It should be 4.
> 
>>>>>> Empirical('1200.0').significance
>>> 5
>> What about when 1200 is actually 4 significant digits? Or 3?
> 
> Then you shouldn't write it as 1200.0. By definition, zeros on the right are
> significant. If you don't want zeroes on the right to count, you have to
> not show them.
> 
> Five sig figures: 1200.0
> Four sig figures: 1200
> Three sig figures: 1.20e3
> Two sig figures: 1.2e3
> One sig figure: 1e3
> Zero sig figure: 0

That last one is not true; 0 is a one-significant figure estimate, and 
represents a value between -0.5 and 0.5.  (It's true that zeroes to the 
left are never significant, but not when there's nothing in the figure 
but zeroes.)

A zero-significant figure would be an order of magnitude estimate only. 
  These aren't usually done in the "e" scientific notation, but it would 
be something like 10^3 (if we assume ^ is exponentiation, not the Python 
operator).

c^2 is 9 x 10^16 m^2/s^2 to one significant figure.  It's 10^17 m^2/s^2 
to zero (order of magnitude estimate).

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