Question

Help with unit conversion? "squared" and "cubed" confusing me!

Answer 1

I understand how to go from cm to m.
But from cm^2 to m^2 ???

E.g.
Go from 500cm^2 to m^2 I got 0.5m^2 but apparantly it's 0.05m^2.

I don't understand why this is.

Answer 2

\[[\text {cm}]=10^{-2}[\text m]\]

\[([\text {cm}])^2=(10^{-2}[\text m])^{2}=10^{-4}[\text m]\]

Answer 3

\[\large 1 m ^2 = 100cm \times 100cm = 10,000 cm^2\]

Answer 4

So if you have 500cm^2, you need to divide by 10,000cm^2 to convert to m^2 \[\large 500cm^2 \times \frac{ 1m^2} {10,000 cm^2}\]

Answer 5

So the squared sign in the unit is taken into account of the calculation? I thought it was just showing whether of not the object is flat or has a volume (if that makes sense)?

Answer 6

For m^3 \[\large 1 m^3 = 100cm \times 100cm \times 100cm = 1,000,000 cm^3\] If you have 500cm^3, then \[\large 500cm^3 \times \frac{ 1m^3} {1,000,000 cm^3}\]

Answer 7

@FollowTheFez yes, since 1m=100cm and \[\large 1m^2 = 1m \times 1m = 100cm \times 100cm\]

I remember being confused by this at some point in school too.

Answer 8

\[500[\text{cm}]^2=500(10^{-2}[\text m])^2=500\times10^{-4}[\text m]=0.05[\text m]\]

Answer 9

Ah, makes sense now. That's why I keep getting them wrong! Thank you! :)

Answer 10

(i also remember finding this unintuitive when i was first learning it)

Answer 11

Yep, i thought if \[\large 1m^2 = 100cm^2\] before realizing it's really \[\large 1m^2 = (100cm)^2\] Makes sense when you think of a square

Answer 12

The brackets make it easier to see. Didn't realise you could write it like that!

Answer 13

\[[\text {m}]=10^{6}[\text{μm}]\]
\[2[\text {m}]^3=2(10^6[\text{μm}])^3=2\times10^{18}[\text{μm}]^3\]

Answer 14

btw @UnkleRhaukus you should use "large" or "LARGE" in front of the latex to make the small latex easier to read:

large 2[\text {m}]^3=2(10^6[\text{μm}])^3=2\times10^{18}[\text{μm}]^3

\[\large 2[\text {m}]^3=2(10^6[\text{μm}])^3=2\times10^{18}[\text{μm}]^3 \]

LARGE 2[\text {m}]^3=2(10^6[\text{μm}])^3=2\times10^{18}[\text{μm}]^3
\[\LARGE 2[\text {m}]^3=2(10^6[\text{μm}])^3=2\times10^{18}[\text{μm}]^3 \]

Answer 15

just zoom in [command] [+]

Answer 16

You can also click the latex to zoom, but for people who're unaware of that, it makes it easy to read.

Answer 17

\[\Huge{\text {OK}}\]

Answer 18

\[\Huge great!\]

Answer 19

\[\Huge \text T\\
\huge \text{h i}\\
\Large \text {s i s }\\
\large\text{n o t a }\\
\text{n e y e t} \\
\scriptsize\text {e s t t h i s i}\\
\Tiny \text {s a n e y e t e s t}\\ \tiny {\$\,\alpha\,\nu\,\delta\, m \,0 \,n\,\varsigma\,\tau\,\alpha}\]

Answer 20

\[\Tiny \text{i cheated by zooming}\]