# 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, 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 from one of the organizations which created the SI units, the BIPM.

• In short, by $cm^3$ we mean $(cm)^3$, not $c(m^3)$ – Nicolau Saker Neto Feb 13 '15 at 17:58
• If I were you, I would have only written: In short... ;) – It's Over Feb 13 '15 at 22:01

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

• Forgive me, a few hours ago I read your answer improperly and mistakenly downvoted you, even though it is correct. The site doesn't allow me take it back after two hours unless you edit your answer somehow. – Nicolau Saker Neto Feb 13 '15 at 18:00
• Though not explained, it isn't incorrect. I don't vote correct answers down. Now. That'll wash it a bit away. – It's Over Feb 13 '15 at 22:03

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

• You can use MathJax to better format your posts. – HDE 226868 Feb 13 '15 at 16:19