I really appreciate the straight forward explanations. It does a good job at putting things into scale/perspective. However, I'm not convinced that discrepancies this small are always "close enough". Consider the Patriot Missile Failure [1] (which has been discussed plenty here on HN [2]). The system's clock was off by about 0.000000095 decimal, but that was enough to result in catastrophic failure. I'm sure that this NASA post is intended for the layperson (which is good), but I'd hope that engineers have a bit more "involved" way of determining the appropriate number of decimals for any given applicaiton?
The article doesn't mention it but adding precision doesn't help for another reason: space isn't flat. If you calculate the surface area of the earth or sun or whatever with pi you're off. Doesn't matter how many decimals you use. You're off because gravity distorts space.
Aren't electrons about 3 orders of magnitude smaller than a sub-atomic particles like protons? And I can't find an estimate of the diameter of a neutrino easily from google (do we even have one?), but it seems like neutrinos are even smaller still. And I think we still have a lot to discover in this area.
So maybe it's more like, about 40-50 orders of magnitude, but potentially much more as we explore the "extremely tiny" portion of the scale?
[1] https://www-users.cse.umn.edu/~arnold/disasters/patriot.html
[2]https://hn.algolia.com/?dateRange=all&page=0&prefix=false&qu...