There is a related issue of the feasibility but impracticality of exactly representing irrational numbers like sqrt(2), independently of the base. And of course transcendentals can never be represented exactly. The most insidious aspect of this is in 3-d modeling, where it’s often necessary to test if a point is above, on, or below a plane defined by 3 other points. The effect is sometimes to create triangles with a missing edge, which can wreak havoc on structural analysis software.
Oh my God, now I really feel stupid