A while back, I had a discussion with our development team about significant figures. Specifically, the discussion centered around where they were going to go to lunch and when they were going to leave. Someone piped in with, “Right here, right now,” while another countered, “I wonder how many significant digits you should take for that to actually be true…” The first dev then stated, “First, you would need some units,” at which point I jumped into the conversation claiming, “Actually, I’m not sure that you do. Whether you are using AU or attometers, the number of significant digits should be the same.”
The conversation then turned to whether significant digits were unit dependent. Keeping in mind the absurdity of the conversation, and the origin that it was spawned from, I actually found the concept really interesting. Are significant digits unit dependent?
The claim that they are not seemed intuitively true to me, but I didn’t have a proof ready to go.