We should write (cm)^2

Seriously, the c (centi, or 1/100) should be squared, otherwise it makes no sense. Let’s say something is 10 cm x 10 cm. That is:

    \[10 \frac{1}{100} \mathrm{m} \cdot 10 \frac{1}{100} \mathrm{m} = \frac{1}{100} \mathrm{m}^2\]

Whereas 100 cm2 would be

    \[ 100 \cdot \frac{1}{100} \mathrm{m}^2 = 1 \mathrm{m}^2,\]

which is clearly not the same. Hence we should write

    \[100 (\mathrm{cm})^2\]

and all our problems are solved, yay! This of course goes for all other SI prefixes.

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