“Getting the right answer” doesn’t really describe numerical analysis. I’d have said “Recognizing when you’re going to get the wrong answer, and getting a controllable upper bound on how wrong”. The book you list seems typical: only one chapter even begins by discussing an exact rather than an approximate method, and the meat of that chapter is about how badly the error can blow up when you try to use that method with inexact floating-point arithmetic.
“Getting the right answer” doesn’t really describe numerical analysis. I’d have said “Recognizing when you’re going to get the wrong answer, and getting a controllable upper bound on how wrong”. The book you list seems typical: only one chapter even begins by discussing an exact rather than an approximate method, and the meat of that chapter is about how badly the error can blow up when you try to use that method with inexact floating-point arithmetic.