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Toot

Written by Freya Holmér on 2024-09-21 at 13:07

oooh km² means (km)² not k(m²) lol

so that's why 1 km² = 1 k²m² = 1000² m² = 1,000,000 m²

I was always like "yeah km² has some wild scaling factor for whatever reason" without ever looking into how it mathematically works out

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Descendants

Written by KING Calyo Delphi on 2024-09-21 at 13:14

@acegikmo Oh, yeah, the SI prefixes are attached to the hip of the unit to make it all one unit.

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Written by Robin on 2024-09-21 at 13:17

@acegikmo Not so fond memories of spending like 30 minutes trying to explain this to someone before giving up.

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Written by George Marques :godot: on 2024-09-21 at 19:01

@Robin_Van_Ee @acegikmo I wrapped my head around this by thinking that 1 km² is a square with 1 km side (and not 1000 squares with 1 m side, so not 1000 m²). Same approach for cubes.

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Written by Professor_Stevens on 2024-09-21 at 13:17

@acegikmo

Could be worse. Wall Street and the financial press abbreviate "million" as "m," but also as "mm" (thousand-thousand). Scientists use "m" to denote 1/1000th of something, like 1 ms being one millisecond. Of course, they also use "m" to mean "meter," and "mm" to mean "millimeter." So 1mm² gets pretty dicey if you don't know whether you're talking to a banker or a biologist.

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Written by cognitively accessible math on 2024-09-21 at 13:21

@acegikmo That's part of our 072 "Math literacy" course. I show the scale factor with feet and yards first 'cause it's small, then get out the meter sticks.

 An excellent lesson "in place value"  takes one little number block and squares and cubes it 'til the person is "1 in a million" in a cube that would fit them all in there. 

(But we're being told we should dump everybody straight into college stats and let 'em Work Harder, rather than build a foundation of understanding first... even though the pass rate is better but still dismal doing that...)

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Written by Benjamin on 2024-09-21 at 13:33

@acegikmo yeah that's something that annoyed me a lot in school when id directly try to convert area using a direct step, then the teacher would go that the multiplier was also squared alongside the unit and it's also never explicitly stated anywhere atleast how I remember it and it's something that I always have to keep in mind when trying to abuse scientific notation to speedrun calculations

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Written by j5v on 2024-09-21 at 15:58

@acegikmo UK: "square kilometers" vs "kilometers squared"

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Written by F4GRX Sébastien on 2024-12-26 at 09:31

@j5v @acegikmo both are ok, what doesnt work is kilo squaremeter 😅

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Written by Willem Janssen on 2024-09-21 at 17:27

@acegikmo This is also related to the square cube law:

Why does a 1 cm³ cubic mouse with 6 cm² skin cool off faster than a 1 m³ cubic elephant with 6 m² skin?

Cause the elephant only has 60,000 cm² of skin, while 1 million mice (1 m³) have 6,000,000 cm² of skin (unless they snuggle up into a cube ofc).

(Square cube cause it’s 100² vs 100³; see wiki for further details, such as why elephants have elephanty legs rather than anty legs.)

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Written by Xeno the CaveSpider 🕷 on 2024-09-21 at 19:32

@acegikmo woah thanks, that makes so much sense now

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Written by Seg on 2024-09-21 at 20:49

@acegikmo personally I usually think of the "k" as belonging to the "number part" and the "m" as belonging to the "unit part". I do the math on these separately when doing unit analysis, and it works out

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Written by Freya Holmér on 2024-09-22 at 14:18

@seg but then the square looks like it should only apply to the units and not the numbers, which would be off by a factor of 1000

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Written by Matt McIrvin on 2024-09-25 at 12:53

@acegikmo This is one of those things I assimilated so long ago that I forget that it's tricky and confusing, so someone getting tripped up by it is a good reminder.

This is why it's useful to have separate metric volume units even though technically you don't need them. With volume, the ratios on length units are cubed. A milliliter is the same thing as a cubic centimeter. That always struck me as a little weird. But it works out: a liter is a cubic decimeter, which is 1/1000 of a cubic meter, and a cubic centimeter is 1/1000 of that. A millionth of a cubic meter, but only a thousandth of a liter.

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Written by K. Sahdra on 2024-09-25 at 15:51

@acegikmo

Btw, what did you think of cm^3 - cubic centimeter?

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Written by Ozzelot :anarchy: :linux: on 2024-09-25 at 17:40

@acegikmo And he’s here to do some business with the prefix on his hip

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Written by F4GRX Sébastien on 2024-12-26 at 09:25

@acegikmo square kilometer tells everything!

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