Calculator Accuracy & Usefulness

[Claudio L.]

(05-25-2015 09:57 PM)Garth Wilson Wrote:  I would say very little of engineering is that way though.

Not as little as you may think. Structural or mechanical engineering problems can pile up nodes and degrees of freedom like it's nothing, and matrices grow huge even for simple problems.
Yes, you can design a crane on the back of a napkin with an approximated method and a slide rule, and get a decent approximation, but if you put the crane in modern design software, it creates a model with several hundred nodes and solves a large sparse matrix doing thousands of operations. If you forced the software to work with 3 or 4 digits, you'd get a much worse approximation than the slide rule. The moment you use modern "generic" methods that don't have specifically targeted simplifications, internal precision becomes more important to guarantee numeric stability.

In electronics, almost any PCB board with a fast clock needs to be ran through a finite element program to determine electro-magnetic interference between adjacent tracks.
It's not something perceptible to humans, like your audio examples, but a CPU running at GHz speeds can't tolerate that a bit gets randomly flipped on a track. In the past, this didn't matter because speeds were slower and components and tracks were much larger.
As things get faster and smaller, we need more numerical digits with more advanced methods to properly design, fabricate and even operate our engineering creations, and this is a lot of the engineering being done today.