Ages ago, when I was in college, a "numerical methods" course was more or less obligatory... has that changed?

Anyway, toying with a slide rule is a fun way of making these things very obvious, because you are essentially working with something like 3-digit floating point. When you find yourself subtracting 1.234 from 1.235, but you know that both the "4" and the "5" are really fuzzy around the edges, it becomes obvious that the resulting 0.001 does not really mean much. Similarly, when you take 1.234e+6 (again with a really fuzzy "4") and add 2, you realize that 1.234002e+6 is not really a sane answer.