> Yes never, not in school, not in analysis, and certainly not in numerical analysis.

Weird, I just assumed that was normal in most education systems. I don't know how you'd get a sense of the rough scale of various common irrationals, without having some idea what they look like when represented in decimal notation. Such representations are normal starting not later than when we start seriously working with circles, in US school, and never really stop coming after that. Estimation exercises lean heavily on having some idea of the decimal representation.

> You've proved my point. It's either π or 3.14. Except that the latter is a rational number :)

Never claimed π is 3.14, so no, I didn't at all prove your point. I wrote that it's very well known that it starts that way. When a normal person says "decimal number" they mean to include π, because any usefully-precise decimal representation of it's going to involve a decimal point. At least in the US, they saw it represented "3.14..." or "3.1459..." or whatever, many, many times in school. It's obviously, to a non-mathematician, a "decimal number". They mean "the real numbers" (or, perhaps, depending on context, exclusively the parts of the reals that aren't whole integers), except that name is harder to remember than the incorrect (but more common and intuitive) "decimal numbers".