Here is a fun fraction from Richard Feynman. I use this as an illustration whenever I talk to my engineering students about significant digits and uncertainty.
1 / 243 = 0.00411522633744855967...
I tell my students their answers should not look like that result. I remember as an undergrad engineering student wanting to be very exact and as a result would compute the design moment or capacity of a beam as something like:
452.83726583243 kip-ft
Nevermind that:
- I guessed the design load.
- I have no idea how the owner will use it (a la the sinking libraries myth).
- I applied a statistically determined factor of safety to the design load I guessed.
- I probably used a simplified elastic analysis (i.e. FEA).
- My analysis used material properties that will differ from those constructed.
- I probably didn’t account for construction tolerances.
- Any precision beyond 3-4 sig figs are likely numerical artifacts with no meaning.
So, all things considered, I think it’s okay to report the beam’s capacity as a cool 450 kip-ft. This is why you learned about significant digits in high school chemistry.