This article says that NASA uses 15 digits after the decimal point, which I’m counting as 16 in total, since that’s how we count significant digits in scientific notation. If you round pi to 3, that’s one significant digit, and if you round it to 1, that’s zero digits.
I know that 22/7 is an extremely good approximation for pi, since it’s written with 3 digits, but is accurate to almost 4 digits. Another good one is √10, which is accurate to a little over 2 digits.
I’ve heard that ‘field engineers’ used to use these approximations to save time when doing math by hand. But what field, exactly? Can anyone give examples of fields that use fewer than 16 digits? In the spirit of something like xkcd: Purity, could you rank different sciences by how many digits of pi they require?
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”