I was telling a student about how Hubble initially overestimated his namesake constant by almost an order of magnitude, and how this wasn't easily corrected. Rather than one experiment correcting the overestimate, later authors may have had some shyness about disagreeing too much with the earlier results and it took about 30 years for H_0 to converge to the modern value. The student asked me something like, "Would it have made a huge difference if Hubble knew? If you could tell Hubble in 1920 that his constant should be closer to 70 km/s/Mpc?"

I didn't have a good answer and thought there would probably be more useful ways to spend that wish, but I couldn't immediately think of any. For example, would telling someone in the 1970s the mass of the Higgs have made much of a difference? I think the hypothetical can be rephrased as a less silly question for those who prefer: was there any point in the history of physics that someone's progress was significantly stalled by lack of data and it would have been highly consequential if one number was known sooner?

It's open ended, so don't overthink the constraints. (Does the recipient know it's from the future, would they have to recognize it from the first 3 or 4 sig figs, would you be able to include units or any other explanation). Interpret however you want.