Because infinite numbers are not a natural expression of discrete measurements, and when it comes to being price 1/3 = 4 is always going to be easier to put your finger on than 1/3 = 3.333.

I work in software and data analysis in the construction industry. A continuous measurement is good for some things, but it's definitely not good for discrete measurements. Furthermore, a lot of the people who work in the field for construction greatly prefer Imperial for a reason. They have no bias towards systems beyond what works fast and easy.

I work a lot with wood in the metric system and the third thing is bot a problem at all. I never had even remotly any trouble finding 333.33 mm or a 666.66 on a tape measure. For anything that needs extreme accurcay I’d go with my iron ruler with 0.1 mm ruling and beyond that I would go for a caliper.

If you consistently have to use a weird measurement over and over again, you usually end up making a temporary ruler (paper, wood, metal) anyways

What is stopping people from making meter sticks with 3000 lines, i.e. every third of a millimeter is marked?

(The point is, there is nothing any more "infinite" about the rational number 1/3 than 1/4, 1/5, 1/2 or what have you. It just can't be written in the arbitrary base 10 system, just like 1/5 can't be written in base 12)

There is nothing stopping you from writing 1/3 meter.

> and when it comes to being price 1/3 = 4 is always going to be easier to put your finger on than 1/3 = 3.333.

Am I missing something? Wouldn’t it just be putting your finger on the 10 cm mark? This is approx 4”.

I realize this is not exact conversion, but it’s trivial to come up with examples where metric is easier: say you have a piece of wood 7 7/8” long that you want to cut in half. Is it easier to put your finger on 3 15/16” or 10 cm?

"price" is an autocorrection of "precise"