Can’t be that big, as the difference in mass close to the instrument only varied in the several tons category, but obviously enough to puzzle the scientists.
Rounding of constants always depends on what you are calculating. Getting a rocket into orbit is a case to use the actual local value of g with a bunch of digits (and the change with height, too). If you build a precision tool, some more digits of PI are no bad idea.
But to calculate the lenght of fence to buy to surround a round pond, I actually used 10/3 for “PI plus safety margin” once.
Just don’t make the same mistake as one physics lab did. They made a series of measurements and their results showed that gravity quickly increases in fall, falls slowly over winter, and back to about pre-fall levels very slowly in summer. It took quite a while to figure out the reason of this unexpected result. They turned their equipment inside out to find a mistake to no avail. Then they realized that the university stored coal for the central heating and hot water in the basement under the lab…
Now that insurances against natural disasters start costing a fortune in places like Florida, and you probably have to have such an insurance to get a mortgage there, it, the costs for housing down there will probably skyrocket soon.