# How many milliliters are in a cubic meter?

Dec 4, 2016

#### Explanation:

$1 \cdot m L$ $=$ $1 \cdot c {m}^{3}$, are we agreed on this?

But $1 \cdot c {m}^{3}$ $=$ ${\left(1 \times {10}^{-} 2 \cdot m\right)}^{3}$, because the $\text{centi prefix}$ $\equiv$ ${10}^{-} 2$.

And thus ${\left(1 \times {10}^{-} 2 \cdot m\right)}^{3}$ $=$ $1 \times {10}^{-} 2 \cdot m \times 1 \times {10}^{-} 2 \cdot m \times 1 \times {10}^{-} 2 \cdot m =$

$1 \times {10}^{-} 6 \cdot {m}^{3}$

And so finally, $\frac{1 \cdot m L}{1 \cdot {m}^{3}} = \frac{1 \times {10}^{-} 6 \cdot {m}^{3}}{1 \cdot {m}^{3}} = {10}^{-} 6$.

Alternatively (finally again) $\frac{1 \cdot {m}^{3}}{1 \cdot m L} = \frac{1 \cdot {m}^{3}}{1 \times {10}^{-} 6 \cdot {m}^{3}} = {10}^{+ 6}$.

Thus there are ${10}^{6}$, $\text{one million}$, $m L$ in a $\text{cubic meter}$.

We use the same methodology to show that there are $1000 \cdot L$ in a $\text{cubic meter}$. A ${m}^{3}$ is a VERY large volume.