what is the proper way of writing 1 square millimeter?

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(.001m)^2 or (.001m^2) I think it is the first one but Im not sure. Please look over these equations for me so I can have a sufficiently long question to submit.

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I believe the second one is the correct one.

The first one makes it look like you are squaring $.001$ as well

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"1 square millimeter" is usually written $1\ \mathrm{mm}^2.$ This is the area of a square whose side is $1\ \mathrm{mm}.$

If you want to convert to square meters, $1\ \mathrm{mm}^2 = 10^{-6} \ \mathrm{m}^2.$

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$1 mm = 0.001 m$

You can square both sides: $1 mm^2 = 0.000001 m^2$