Well, just think “How would I do this cheaply and get away with it” for a good enough “Engineering” approach for this case.

The really expert “Engineering” stuff related to things like maintenability, reliability, robustness and so on (which I myself am not qualified to talk about, as even though I have an EE degree, that’s not actually the domain of Engineering I ended up working in so I haven’t accumulated the professional experience that teaches one to take such higher level considerations into one’s designs), isn’t, IMHO, really necessary to understand to explain why those designing circuits commercially would chose the commonly available and cheaper components if they can.

There’s an old saying that engineers measure with a micrometer, mark with a grease pen, and cut with a hatchet. You do the math right first, check the tolerances and tools at hand, then you try whatever seems like it’ll work keeping room for your second and third guesses. Never give the boss their company credit card back until you’re pretty sure you won’t need another hardware run of the day.

The actual method for calibrating exact resistor values involves starting with a lower resistance and etching away parts of it with a laser to get to the exact value you want. You probably still couldn’t get as many decimal places as OP tho

Note that if it’s a series circuit you simply add resistance.

I’m just an electrician though, we don’t actually use the math or the theoretical stuff terribly often

Ohh, I remember this from uni physics class. I guess I just don’t know how to apply it in any practical sense though. Lol Thanks for reminding me!

deleted by creator

A failed inspection is just an invitation to use a different method until it passes.

For back-of-the-envelope or mental calculations, pi is often 3 or 10^(1/2).

The latter is better than 1% accurate, and has nice properties when doing order-of-magnitude/log space calculations in base 10.

There’s less and less reason to do it (and it’s never 5). On systems without floating point you might want to round it a bit, but only if the specific thing you’re doing allows it, and even then you’re more likely to do a fixed-point approach by using e.g. 314 and dividing by 100 later, or adjusting that value a bit so you can divide by 128 via bitshift if you’re on a chip where division is expensive. However, in 2025 you almost certainly should have picked a chip with an FPU if you’re doing trigonometry.

And while rounding pi to 3 or 4 is certainly just a meme, there are other approximations which are used, like small-angle approximations, where things like sin(x) can be simplified to just x for a sufficiently small x.

There’s a lot of weird stereotypes out there that make no sense. Like the whole “programmers wear thigh high socks” thing. Where did that even come from?

you’ve never seen anybody simplify it to 3 when doing head calcs without a phone nearby?

it doesn’t happen often, in fact I’ve seen it once. in a decade.

Can confirm, am shaped like a weird donut

Nope, same problem as linear. Can you get angle correct to 4 decimal places and prevent the contact from oxidation?

“Digital potentiometers” are rotary encoders, which are switches, not resistive dividers. They are a useful input device for a microcontroller but not in an analog circuit.

Another option is a multi-pole rotary switch with selectable resistors in each position, but that only gives you the available values.

They are all larger and more expensive. Just use two E12 resistors in parallel or series, you can always get within 1 %. They cost a dime a dozen. The series was made for such combinations – did you know that 180 Ω and 220 Ω in parallel gives 99 Ω, a value useful for 1/100 dividers?