One of the things that most mathematicians and science related people miss, are the relative accuracy of numbers. From the very beginning almost everyone is taught to operate on numbers and assume they are all absolutely exact, which they rarely are. If you are making marbles Pi to two decimal places is fine; if you are making bearings for jet engines you may want a few more decimal places to insure everyones safety.
Surprisingly, you see engineers and scientists fall into the trap of using the most accurate of two numbers when making a calculation when the least accurate dictates or worst yet the errors compound and less accuracy is achieved, since neither was exact to begin with. In engineering design this is compensated for in any number of ways. I do not know what the Theory and Hypothesis guys do.