Kirnbichler wrote:
The foot is as arbitrary as the meter.
That's true, but ... that's not the point. Metric means that every measure can be constructed out of this basic unit.
You can make the same argument with Imperial units. Metric uses base ten, always, that’s the key.
We had 12 pence in one shilling, two shillings in one farthing, 10 farthings or 20 shillings in a pound.
16 ounces in a pound, 14 pounds in a stone, 8 stone in a hundred weight.
12 inches in one foot, three feet in one yard, 1760 yards in one mile.
It’s all perfectly logical and clear. I’m sure you agree.
Areas are measured in square metres, volumes are measured in cubic metres (and/or multiples or fractions thereof, these multiples or fractions being powers of ten and such easy to understand).
1 metre (m) is 10 decimetres (dm) or 100 centimetres (cm) or 1000 millimetres (mm)
1 decimetre (dm) therfore is 10 centimetres (cm) or 100 millimetres (mm)
1 kilometre (km) is 1000 metres (m) and therefore 1 million millimetres (mm)
1 millimetre (mm) is 1000 micrometres (µm)
1 cubic metre (m³) is 1000 cubic decimetres (dm³) or litres (l)
1 litre is 1000 millilitres.
1 millilitre is a cube with a side length of 10 millimetres or 1 centimetre, hence 1 millilitre is 1 cubic centimetre (cm³).
A body with a density of 1 gram per cubic centimetre and a volume of 1 litre weighs 1000 grams (or 1 kilogram).
A body with the same density, but a volume of 1 cubic metre weighs 1000 kilograms or 1 ton.
Water has a density of 1 gram per cubic centimetre.
(depending on temperature, salinity etc., but precisely enough for people to understand that a bottle with a content of 1 litre weighs 1 kilogram more when full instead of empty).
Compare this arbitrary system to the entirely logical and clearly structured system in the US:
1 mile is 5280 feet or 63360 inches
1 gallon is 231 cubic inches
1 cubic inch is 0,554113 fluid ounces.
1 pound is 16 ounces
1 fluid ounce of water weighs a bit (about 4.3%) more than 1 ounce
And there are two different feet:
https://www.nytimes.com/2020/08/18/science/foot-surveying-metrology-dennis.html