Are you reading "to a first approximation" as "to one significant figure"? I thought it meant something like "using the lowest order function which is an accurate fit to the data". So, to a first approximation, pi is roughly 22/7, and to a first approximation, the distance to Earth's horizon in kilometers is 3.57 times the square root of the height above sea level in meters.

To say that "to a first approximation, all biologists believe in evolution" is, by this definition, to say that the fraction of biologists that don't is so small that it is not easily measured. I believe this to be the case because that fraction is so small that it is significantly affected by the choice of definition of "biologist".

Yes, but my "nth approximation" module only has settings for "zeroth" and "first".