A friend recently remarked that every time he went for a jog, he lost a pound, presumably through sweat. I asked how he knew this and he said it was simple: he weighed himself before the run, and the scale read 200; when he came back and reweighed, it said 199. I was going to explain to him that he could have weighed 200 plus a tiny bit before, and 200 minus a tiny bit afterwards, meaning a very small difference in truth, but decided to just say “that's interesting”. No need to bring up the ±last digit uncertainty issue, I figured.
But his conclusion made me think. Even though any analog or mixed-signal designer who understand the basics knows that accuracy, precision, resolution, and repeatability are important parameters which affect the validity of a reading, and how it can be used, the other half of our brain may not be so insightful or aware of that reality.
We see a number, whether it is a basic weight on a scale, or voltage readout for our AC line (I have a miniature, application-specific DPM that plugs into a line socket and shows the line voltage, to three significant figures) and we remember that number, period. We really don't think abut what it means, or that the difference between “199” and “200” may be a tiny value, not a full unit.
We easily fall into the same trap that non-engineers may have, and we have no excuse except that we, too, are humans, with a brain wired to see and work with summary data to the first-order approximation. (Of course, a digital readout only encourages this sort of quick assessment, compared to the more vague analog indicator, which admittedly is better for trend-watching.)
This tradeoff is probably a good thing because over-thinking can impede a fast response, and, sometimes, the quickness of our response is more critical to survival and success than a better but slower conclusion and response, At the same time, when circumstances require it, and time allows, it's a good idea to step back and look at what those digits represent in terms of true meaning and implication, ♦