# Why is a 1*dm^3 volume equivalent to 1*L?

Oct 3, 2016

$1 \cdot {\mathrm{dm}}^{3} \equiv 1 \cdot L \equiv 1000 \cdot c {m}^{3} \equiv {10}^{-} 3 \cdot {m}^{3}$.

#### Explanation:

$d$ is the abbreviation for $\text{deci} = {10}^{-} 1$.

Thus $1 \cdot {\mathrm{dm}}^{3}$ $=$ ${\left(1 \times {10}^{-} 1 \cdot m\right)}^{3}$ $=$ $1 \times {10}^{- 3} \cdot {m}^{3}$

$c$ is the abbreviation for $\text{centi} = {10}^{-} 2$.

And $1 \cdot c {m}^{3}$ $=$ ${\left(1 \times {10}^{-} 2 \cdot m\right)}^{3}$ $=$ $1 \times {10}^{- 6} \cdot {m}^{3}$

And thus there are $1000 \cdot c {m}^{3} \cdot {\mathrm{dm}}^{-} 3$, or $1000 \cdot c {m}^{3} \cdot {L}^{-} 1$

And there are also $1000 \cdot L \cdot {m}^{-} 3$. A $\text{cubic metre}$ is a very large volume.

And thus $1 \cdot m o l \cdot {\mathrm{dm}}^{-} 3$ $=$ $1 \cdot m o l \cdot {L}^{-} 1$, which is the familiar unit of concentration.

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