How many square millimetres are in 0.000075 square metres?

Question

Doing my head in a bit..

$0.000 075 \times 100$ = in square cm, and times that by $10 =$ square mm but apparently I'm off by a couple of orders of magnitude.

Answer 1

We know that $1 \, \mathrm{m} = 1000 \, \mathrm{mm}$ so, squaring both sides yields $$1 \, \mathrm{m}^2 = 1000^2 \, \mathrm{mm}^2 = 10^6 \, \mathrm{mm}^2$$

That is, one square metre is equivalent to $10^6$ square millimetres. Therefore $$0.000075 \, \mathrm{m}^2 = 0.000075 \times 10^6 \, \mathrm{mm}^2 = 75 \, \mathrm{mm}^2$$

Or that there are $75$ square millimetres in $0.000075$ square metres.