Why does 1 cubic meter = 1000000 cubic centimeters?

I have the SI chart in front of me. It states that a centi is 10^-2 and since they are already designated cubic meters why does 1 cubic meter equal 1000000 cubic centimeters?




Take a look at the Wikipedia article for [SI prefixes](http://en.wikipedia.org/wiki/Metric_prefix), in particular, the following excerpt:



> 
> When units occur in exponentiation, for example, in square and cubic forms, **the multiplication prefix must be considered part of the unit, and thus included in the exponentiation**.
> 
> 
> * $1\ km^2$ means one square kilometre, or the area of a square of $1000\ m$ by $1000\ m$ and not 1000 square metres.
> * $2\ Mm^3$ means two cubic megametres, or the volume of two cubes of $1000000\ m$ by $1000000\ m$ by $1000000\ m$ or $2\times10^{18}\ m^3$, and not 2000000 cubic metres ($2\times10^{6}\ m^3$).
> 
> 
> 


Thus, the relationship between the cubic metre and the cubic centimetre is as follows:


$$1\ m^3 = (1\ m)^3 = (100\ cm)^3 = 100\ cm \times 100\ cm \times 100\ cm = 1000000\ cm^3 = 10^6\ cm^3$$


$$1\ cm^3 = (1\ cm)^3 = (0.01\ m)^3 = 0.01\ m \times 0.01\ m \times 0.01\ m = 0.000001\ m^3 = 10^{-6}\ m^3$$


For a real case, converting $243.7\ cm^3$ to $m^3$ step by step:


$$243.7\ cm^3 = 243.7\times 1\ cm^3 = 243.7\times (1\ cm)^3 =243.7\times (0.01\ m)^3 = 243.7\times 0.01\ m \times 0.01\ m \times 0.01\ m = 243.7\times 0.000001\ m^3 = 243.7\times 10^{-6}\ m^3 = 2.437 \times 10^{-4}\ m^3$$


This is simply the way it was defined, and it is the standard everyone adheres to. More examples of SI prefix usage can be found on [this page](http://www.bipm.org/en/publications/si-brochure/chapter3.html) from one of the organizations which created the SI units, the BIPM.


 4

$1\ \texttt{m}^3$ is equal to $(\texttt{100 cm})^{3}$ because $1\ \texttt{m}$ is equal to $100 \ \texttt{cm} = 10^2\ \texttt{cm}$.


 1

1 cm = $10^{-2}$ meter


i.e 1 m = $10^2$ cm


So 1 $m^3$ = $(10^2)^3 cm^3$


i.e 1 cubic meter = $10^6$ cubic centimeter


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