> How do you measure your string or the diagonl of the square?
By the string! How do you measure “1”?! same way. We are talking lengths, not abstract numbers.
Yes, 3 for Pi is often good enough, except in the Rav Yohanan’s puzzling statement.
Greeks were very disturbed when they realized that there are irrational numbers (I think it was sqrt(2)). I don’t think Jews have same concerns about rationality of the world. Hashem is One, the rest can be counted approximately. (paraphrasing “In G-d we trust, everyone else pays cash”)