> ... found the speed of 3 GeV neutrinos to be 1.000051(29) c.What does the "(29)" in "1.000051(29) c" mean?

 I'm not sure, but I think it represents uncertainty over the last digits.So 1.000051(29) would be equivalent to 1.000051 +- 0.000029.
 Yes, that is what it means. :)
 That can't be it because the error wouldn't straddle the speed of light. It would put the range at 1.000022c to 1.000080c, both of which exceed c, so they wouldn't have written it off as error.
 But that doesn't indicate a hard error bound; this is a statistical matter, after all. Most likely it's just an expected standard deviation.
 It indeed is the standard deviation.
 A single standard deviation is not enough, normal procedure is to allow up to three standard deviations (or more, sometimes five), which puts the measurement in a range consistent with models.
 That means that the last two digits of the number 1.00005129 are uncertain.For example, they measured 1.00005129c, but maybe their uncertainty is +-0.0000001c. The last digits are unreliable, but are the measurements they gotEDIT: below, its claimed that those digits ARE the uncertainty. That quite possibly is it; my answer is from what i remember from uncertainty in my 1st year Physics course.
 Those figures are being provided because they were measured, but they are within the expected experimental error for the device.
 Repeating. It's 1.000051292929292929...edit: sorry if that's incorrect in this case. "1.000051(29)" is one of the formats of indicating repeating decimals, per http://en.wikipedia.org/wiki/Repeating_decimal#Notation

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