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(6.67259 +/- 0.001) * 10^(-11) m^3kg^(-1)s^(-2)
If this is
the way CODATA reported their previous value
(5 places after the decimal with an uncertainty in the
third place after the decimal) then they've not learned
basic rules of reporting uncertainties that I drum into my
students! :)
Maybe it would help to do more thinking and less drumming.
The CODATA team is comprised of the world's leading
metrologists. It might be worth considering the possibility
that they know what they're doing.
In fact there are exceedingly good reasons for reporting data
such that the uncertainty is dozens of times greater than one
count in the last decimal place.
The "significant figures" rules you learned in high school are
completely unacceptable for serious work, for reasons explained
in detail at:
http://www.av8n.com/physics/uncertainty.htm