Is super-accuracy matters?

[johnb]

I think an interesting branch-off discussion (maybe in a different thread?) would be, "how do you convince others that additional accuracy/precision is/is-not needed?" (For various scenarios.) Also taking into account the differences in audiences.

For example, back in the 1990's I found myself stonewalled with a team of fellow software engineers who insisted that double precision floating point (on a 32 bit machine, AFAICR) was sufficient for an accounting suite that was supposed to be able to handle GNP-sized quantities across any of the common world currencies.

I was able to make my point that we should use a variable-digits exact BCD library, by (again like the above) coming up with a few examples that would be off by a few thousand dollars for a company the size of, say, Nestlé. And I made sure I had both the accountant SMEs and the other software designers in the room. The engineers instantly said "oh, that's in the noise for those size transactions" and the accountants just flipped out. And made my argument for me.

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Any other interesting examples of how people successfully (or unsuccessfully) argued one side or the other?