Significant figures calculation

[Erik Max Francis]

Mel wrote:
> Erik Max Francis wrote:
>> Mel wrote:
>>> By convention, nobody ever talks about 1 x 9.97^6 .
>> Not sure what the relevance is, since nobody had mentioned any such thing.
>>
>> If it was intended as a gag, I don't catch the reference.
> 
> I get giddy once in a while.. push things to limits.  It doesn't really mean 
> anything.  The point was that it's only the 2 in a number like 2e6 that is 
> taken to have error bars.  The 6 is always an absolute number.  As is the 10 
> in 2*10**6.

They're not absolute numbers.  It's just that the whole convention 
surrounding significant digits means that the figure is accurate to the 
last significant digit, plus or minus the range that would round to it. 
  That would be true for any base, it's just that we use base 10.

If the error bars are something other than that, they're either written 
down explicitly (they need not even be symmetric), or they're written 
with the convention of using parentheses to indicate the (symmetric) 
error in the final set of significant digits.  For instance, RPP 2010* 
has a figure for Newton's gravitational constant of 6.67428(67) x 10^-11 
m^3/(kg s^2), which means (6.67428 +- 0.00067) x 10^-11 m^3/(kg s^2).

.

* http://pdg.lbl.gov/2011/reviews/rpp2011-rev-phys-constants.pdf

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