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Comment by ISL | Hacker News Reader

A U.S. survey foot is expressed as a fraction — 1200/3937 meters — while an international foot is expressed as a decimal, exactly 0.3048 meters.

A decimal is an alternative notation for a fraction.

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They are still not the same value.

Who has the kind of money to quibble over that fifth decimal place? Oh yeah, national governments.

Assuming the question is serious: Owners of land near the US west coast.

Not near the east coast. US property is measured from a line of reference points near the east coast, so if you use the wrong foot there, your property boundaries will be less than 1mm wrong, and you and your neighbour are unlikely to notice. But near the west coast you may be building your house/fence/whatever 0.5m into your neighbour's land.

I wasn't serious, but this is good information. I assume some of that is a holdover from mineral or oil rights being life-and-death.

No, it's about cities, and it's as old as street networks.

Suppose your neighbour has a 30×30m corner plot and you build a five-story building 50cm onto your neighbour's plot. The street isn't going to move, so you've just reduced the size of his possible six-story building by about 2%, and 2% of the value of a six-story downtown building is worth a lawsuit.

It's the result of how the US handed out land to settlers using survey to hand out square blocks largely sight unseen. However California has grants from the Spanish crown at the root of many of its property deed chains, so the mess will be different.

It can still be very life-and-death if your survey says that the natural gas line is half a meter from where it actually is.

But when they dig it up and it was really half a yard, they're just going to scratch their heads, nobody dies.

Near part of the west coast, there are fairly large effects due to plate tectonics (centimeters per year). I would think western California must have a measurement system whose position relative to points on the east coast gets adjusted periodically, with various deeds recording positions relative to ‘fixed’ points near the west coast.

Only for rational numbers. Decimal -> fraction is a surjection. Irractional numbers, notionally representable as decimals, are uncountably infinite, and do not map 1:1 to fractions.

It is rational: 391/1250

This particular value is, certainly.

(Note: this was a mistyping of 381/1250)

It is literally a ratio of integers, therefore rational.

Correct, rational numbers are those numbers that can be represented as a ratio of integers (excluding zero as denominator). Our points agree.

I think you’re technically equating non terminating to irrational but the looser point seems fair to me— it’s hard to codify precise decimals.

Close. Many non-terminating can be mapped to fractions (e.g. 0.88888... = 8/9), which is equivalent to rational, but non-terminating and non-repeating are irrational (e.g. π or e).

I guess I’m just making the point all nonterninating are hard to codify in non mathematical fonts formatting etc. For instance using that 0.88888 example, that decimal very much does not precisely equal 8/9. you’d either have to keep writing 8s into infinity or hope everybody who copies/Padres your writing has a way to preserve the indicator of repeating digits.

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