this post was submitted on 26 Aug 2023
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That's an idea I would have supported when I was taking high school physics. My astronomy calculations I put to the nearest centimetre (something like 20 significant digits sometimes) for no good reason. Just writing down all the numbers from the calculator.
Then I took engineering and grew out of it. Sure some crucial parts need very tight tolerancing, but you also have to have it relative to the size of the part. And if your design is bad, better tolerancing isn't going to save you from stuff like the steering wheel popping out.
My grandpa once published an article where he turned a tree circumference (obtained using a tape measure) into a "diameter estimate" with 6 significant figures. Turns out, he was wrong on the 4^th^ digit because he used π=3.14...
My high-school chemistry teacher would dock a point for each extra digit past the calculation's actual precision. We learned quickly not to overstate our sig figs.
An answer written as "3" means that the true value is somewhere between 2½ and 3½. If you write "3.19142" when what you actually know is "3", you're incorrectly excluding the vast majority of the possible true values.
Our physics teacher taught measurements and uncertainties as the very first thing in our multi-year syllabus. All answers thereafter needed to be in the precision implied from the number of significant figures in the given figures and error propagation.
The difference between accuracy and precision.
Please tell me you actually had that many digits of significant figures and weren't just copying down overly-specific figures from your calculator...
He most certainly didn't. Other than physical constants, very few measurements were ever taken to more than 15 significant figures. It's just not practical as no instrument will get 1m precision over a light year. A spacecraft travelling anywhere near that far will just get an order of magnitude closer and then recalculate with one more digit of precision.
You are exactly right, and I wasn't copy pasting I was writing it all down as part of pen-and-paper submitted answers. I don't have 1/5 of the energy for such trivial things anymore.
Prof here...it's always the latter.
Yeah it’s one thing to spit out numbers. But as an engineer I have to understand what’s going to happen with thermal expansion, wear and tear, and what can actually be produced consistently by an apathetic worker on their 60th hour of work that week
Wait until you hear about what CS does to run-time complexity. Throw away the constants and small factors, nobody cares!