Princeton on floats has the quote.
Every time you perform an arithmetic operation, you introduce an additional error of at least ε. Kernighan and Plauger: "Floating point numbers are like piles of sand; every time you move one you lose a little sand and pick up a little dirt." If the errors occur at random, we might expect a cumulative error of sqrt(N) εm. However, if we are not vigilant in designing our numerical algorithms, these errors can propagate in very unfavorable and non-intuitive ways, leading to cumulative errors of N εm or worse.
I started rounding off doubles in accounting code in 80 and 81, I switched to integers to run faster.
I learned math by pencil and paper, "gifted" at it. That's how I know what to code.