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Significant Figures: am I a joke to you?
Accurate(closer to the real answer), is not equal to precise(consistent measurements). I think… right?
Yes. I had a science teacher devote a significant portion of a day’s lecture to that exact subject: the difference between accuracy and precision. You got it right.
For example, if you have a digital scale that displays weight to five decimal points, it’s precise. If that scale hasn’t been properly calibrated, though, it will give you a very precise number that isn’t accurate.
It is kind of weird that real world measurements always have error to them so you only really know something to a few digits of precision… but mathematical constants like pi can have effectively have unlimited significant figures (but it’s kind of pointless to have more because any real world applications only need a rather small amount of them). I feel kind of similarly about integration. It’s nice to find a closed form solution for an integral, which can make certain calculations a lot faster and more accurate… but in reality if you’re just solving an integral or two for an engineering project you’re probably better off just computing it numerically to the correct number of sig figs. There’s something a little sad about that to me.