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we have had a discussion on gravitational constant in the past ("New gravitational constant", starting from 22 Jan 2008). However, there is an interesting article in Physics Today on the quest for a better value of G: <http://scitation.aip.org/content/aip/magazine/physicstoday/article/67/7/10.1063/PT.3.2447>
"The search for Newton’s constant" By Clive Speake and Terry Quinn
Among other things, they write that "it appears that we know G to only three significant figures". Astonishing!