> I think you're saying that all physically measurable quantities are rational numbers with terminating decimal expansions.

No, this most certainly isn't true.

For example, take a meter defined (as SI does) as a fraction of the speed of light.

Now, for every length in the universe to be a rational fraction of this length is most certainly not true, because lengths, under relativity, form a continuum. Any speed is possible, so any length (via contraction) is possible.

There'd be no physical reason all physical processes would be constrained to a subset of rational grid points - things can move freely.

Heck, if all physical quantities are rational, are you claiming velocities only occur as rational numbers? That time is only rational numbers?

It's far more likely that they'd be irrational, and our man made units are the weird things.

Suppose two diagonal corners of a square with rational sides are somehow physically exact.... What is the physical diagonal length?

Oh yeah, irrational.

So no, physics isn't formed from rational numbers.