Converting area of a rectangle

Question

This is probably a very simple question and I'm being stupid.

Let's suppose I have a rectangle that is 0.6m by 0.4m. To calculate the area of this rectangle, you do 0.6 multiplied by 0.4, which is 0.24m^2. However, if I convert the units to cm first, to calculate the area you do 60 multiplied by 40, which is 2400cm^2. When I convert this value back into meters the answer is 24m^2. What am I doing wrong?

$100 cm= 1 m$, but $100^2cm^2=1m^2$ – herb steinberg Jun 11 '20 at 15:09 — herb steinberg, Jun 11 '20 at 15:09

score 1 · Accepted Answer · 2020-06-11T15:20:31.720

You seem to be labouring under the delusion that $1\mathrm m^2=10^2\mathrm{cm}^2$, when actually $1\mathrm m^2=10^4\mathrm{cm}^2$ and $10^2\operatorname{cm}^2=1\mathrm{dm}^2$.

So to say, $\mathrm{cm}^2$ stands for the squared centimetre "$(\mathrm{cm})^2$", and not a centi-squaremetre "$\mathrm c(\mathrm m^2)$". As far as I know, prefixes indicating the scaling are always treated as part of the symbol indicating the measure unit, and not as a "separate term" of a monomial. For instance, $\mathrm A\cdot\mu\mathrm{Pa}^3$ stands for ampere times cubed micropascal.

Ah, I see. Consider this marked as an answer, I can't until 10 minutes — , Jun 11 '20 at 15:10

score 0 · Answer 2 · answered Jun 11 '20 at 15:10

0

Note $2400 \ cm^2 = 2400 \ (1 \ cm)^2 = 2400 \ (0.01 \ m)^2 = 2400 \times 0.0001 \ m^2 = 0.24 \ m^2$

answered Jun 11 '20 at 15:10

Vishu

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Converting area of a rectangle

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