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This question is rather historical one.

kilometres can be defined in metres, metres in centimetres, centimetres in millimetres.

There must be some elementary unit (like millimetre or smth.) which cannot be defined in smaller units.

The question is : How does this elementary unit came into being?? e.g. How did scientists decide about exact distance between point A and point B which is considered millimetre??

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"There must be some elementary unit (like millimetre or smth.) which cannot be defined in smaller units." What makes you think so? It's perfectly fine for some choices of base (like the choice of $x$, $y$, $z$-direction) to be arbitrary, and there does not necessarily need to be some canonical "fundamental unit". –  leftaroundabout Jul 23 '11 at 18:18
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This question verges on being a duplicate of Why were the SI base quantities chosen as such?. The choice of units is always somewhat arbitrary, and has generally been driven by practical consideration at the time the choice is made which sometimes leaves us with conventions that seen strange. –  dmckee Jul 23 '11 at 18:57
    
I'd migrate this "question" back to math. –  Georg Jul 23 '11 at 20:09
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migrated from math.stackexchange.com Jul 23 '11 at 17:15

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3 Answers

According to Wikipedia (and I have seen it elsewhere) one part in 10^7 of the meridian through Paris from the equator to the north pole won out over a pendulum with a half period of a second. Nowadays it is based on the speed of light and the definition of the second.

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See SI base unit (and perhaps also history of the metric system) on Wikipedia.

Specifically, kilometres, centimetres, millimetres and other prefixed SI length units are defined as multiples or fractions of the base unit, which is the metre. The definition of the metre itself has varied over time: Wikipedia has an article on that too.

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In the US spelled meter and in France spelled metre. –  GEdgar Jul 23 '11 at 17:22
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Funnily enough, the English Wikipedia chooses to spell like the Brits. And @GEdgar, I thought they spell it "yard" in the US... –  Willie Wong Jul 23 '11 at 17:38
    
@willie: I'm not sure if that was a joke, but yards and meters are not the same length. A meter is about 10% longer. –  Colin K Jul 23 '11 at 17:49
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@Colin: egads, how can that possibly be anything other than a joke? –  Willie Wong Jul 23 '11 at 19:18
    
@willie: the internet is a strange place :) –  Colin K Jul 24 '11 at 0:28
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While the metre (or meter if people prefer) is the SI unit of length I believe the poster is essentially is there a length after which nothing can be smaller. The shortest possible length is probably the Plank length which is a tiny 1.616252(81)×10−35 metres.

IIRC, the meter is currently determined by a certain number of wavelengths of the fundamental emission of a Caesium atom - but don't quote me on that.

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it's now defined in terms of the speed of light and the second. As our measurement of 'c' get better we effectively change the definition of the metre - it's less trouble than changing c or the second! –  Martin Beckett Jul 24 '11 at 22:52
    
The Planck length is not actually a shortest possible length, it's just the natural length scale "identified" by the fundamental constants of physics. There's no physical reason why something couldn't be smaller than the Planck length. –  David Z Jul 24 '11 at 23:09
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