I'm not being smart right now but what does an area density of this mean $$10000 \text{ mm}^{-2}$$
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Per unit area, measured in square millimeters – J. W. Tanner Mar 17 '24 at 18:18
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Sorry I still don't understand, the prefix is at front right and then m^-2? or is it like meter *meter but one of the meters is actually 100 of a meter? – amnna Mar 17 '24 at 18:23
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3It is highly likely that it means $(mm)^{-2}$, and not $m(m^{-2})$. – JonathanZ Mar 17 '24 at 18:33
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2Per convention $\langle \text{prefix}\rangle m^n$ means $(\langle\text{prefix}\rangle m)^n$, and not $\langle\text{prefix}\rangle(m^n)$, so $mm^{-2}$ is an area that is one millimeter in each direction. – Henrik supports the community Mar 17 '24 at 18:33
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1Also, the two ways of interpreting that expression differ by a factor of 1000. If you have any sense of intuition about the quantities being reported, only one of them ought to be sensible. – JonathanZ Mar 17 '24 at 18:36
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There are ten thousands of something on every square millimeter. – md2perpe Mar 17 '24 at 19:12
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but why is the 2 negative? wouldn't one millimeter in each direction just be $$mm^2$$? – amnna Mar 17 '24 at 19:19
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is it this $\frac{(1)}{10000mm^2}$ ? $0.0001mm^2$ ? $0.1m^2$? – amnna Mar 17 '24 at 19:30
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It may be $\frac{10000}{\text{mm}^2}$ like in the inverse square law – Тyma Gaidash Mar 17 '24 at 19:33
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It is 10000 of something per square mm. If it was 10000N of force this would be a pressure. If it were 10000 coulombs of charge this would be a surface charge density. – Paul Mar 17 '24 at 19:41
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oh I understand now, don't even know what I was thinking.. thank you – amnna Mar 17 '24 at 19:46
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There is a stray $-$ in my comment, a square that is one millimeter in each direction has an area of $1 mm^2$. – Henrik supports the community Mar 18 '24 at 18:53
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Recall that a base to a negative exponent is equivalent to 1/the base to that positive exponent. $(x^{-2} = \frac{1}{x^2})$. Acceleration due to gravity is sometimes listed as 9.8m$s^{-2}$ which is 9.8m/$s^2$ or 9.8m/s/s - 9.8 meters per second per second or "per second squared". Area density is usually mass over area though so a unit is probably needed for the 10000.
Nate
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