[thaumasiotes]

> Decimal (or any other numbering system, really) approximations are only useful when you never want to do any further arithmetic with the result.

What? The opposite is the case. Anything you want to do something with, you can only measure inaccurately; arithmetic doesn't have any use if you can't apply it to inaccurate measurements. That's what we use it for!

[qayxc]

So I take it you never wrote any numerical simulations or did symbolic calculations then?

Catastrophic cancellation and other failures are serious issues to consider when doing numerical analysis and can often be avoided completely by using symbolic calculation instead. You can easily end up with wrong results, especially when composing calculations. This would make it difficult to, for example, match your theoretical model against actual measurement results; particularly if the model includes expressions that don't have closed-form solutions.