> but for a meter it requires either going two orders of magnitude (25/100ths for a quarter) or simply cannot perfectly represent the amount (1/3).

What? you switch to metric and suddenly fractions are not a thing any more?

1/3 m is just that, one third of a meter, perfectly. How is that so complicated? It can also be 333.3mm. And no one would write it as 333/1000 to make it seem more complicated than it is.