Engineers and "exact" calculations

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.

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