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From: Matthew Austern (austern_at_[hidden])
Date: 20010904 12:32:13
Kevlin Henney wrote:
>
> > From: Matt Austern <austern_at_[hidden]>
> >
> >I'm more familiar with the very small units than with the very large,
> >but in my experience it's quite common to convert between (say) electron
> >volts and joules, and between meters and bohr radii.
>
> This is true, but the number of significant figures remains the same.
> So, although the magnitudes vary, the floating point floats
> appropriately.
Not quite true, actually, since the conversion factors in these two
examples I gave are measured quantities as opposed to defined
quantites. They have finite precision. For example,
1 eV =1.602176462(63) x 10^19 J, where the digits in parens are
the 68% confidence limits for the last two digits.
If anyone was doing a math library that attempted to keep track of
the accuracy of physical measurements, they'd have to keep this
into account. Sounds like a very hard task, though, since
uncertainties are introduced in lots of different ways and since
they aren't always gaussian.
Incidentally, one good source for numbers like this is
http://physics.nist.gov/cuu/Constants/index.html. Their
numbers come from a roundup of all of the relevant experimental
literature.
Matt
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