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this post was submitted on 12 Mar 2024
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Asklemmy
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Engineering student. I typically use whatever number of digits the calculator gives me in calculator computations, but that's unnecessary. IMO for a design, an engineer should use at least as many digits of pi as needed to not lose any significance due to truncating pi specifically. Practically, this means: keep as many significant digits as your best measurement. In my experience, measurements have usually been good for 3 significant digits.
For back-of-the-envelope or order-of-magnitude calculations where I only need to get in the ballpark of correctness, I'll use 3 (i.e., one significant digit). For example, if I order a pizza with a diameter of 12 inches, A ≈ 36 * 3 in^2 = 108 in^2 is a fine ballpark approximation that I can do in my head to the real area A = 36π in^2 ≈ 113.097... in^2 that my calculator gives me.
I like your idea of using 3 as an approximation to get ballpark figures - if you wanted to add a smidge of extra accuracy to that you can just remember that in doing so, you’re taking away roughly 5% of pi.
0.14159265 / 3 ≈ 0.04719755
Add in around 5% at the end and your approximation’s accuracy tends to gain an order of magnitude. For your pizza example:
108 in^2 x 1.05 = 113.4 in^2 which is accurate to three significant figures and fairly easy to calculate in your head if you can divide by twenty.
You could even fudge it a little and go “108 is pretty close to 100. 5% of 100 is obviously 5, so the answer is probably around 108+5=113”