# How to convert L to dm3 and ml to cm3 Questions: 1) 10cm3 to Gm? 2) 10L to Gm? 3) 10mL to Gm? 4) 10dm3 to Gm?

Dec 1, 2016

$1 \cdot L \equiv 1 \cdot {\mathrm{dm}}^{3}$

$1 \cdot m L \equiv 1 \cdot c {m}^{3}$

#### Explanation:

Both ${m}^{3}$ and $\text{litres}$ are units of volume. There are $1000 \cdot L$ in a $\text{cubic metre}$, which is a very large volume.

$1 \cdot {\mathrm{dm}}^{3}$ $=$ ${\left(1 \times {10}^{-} 1 \cdot m\right)}^{3}$, because $\text{d}$ $\equiv$ $\text{deci}$, i.e. ${10}^{-} 1$.

And thus $1 \cdot {\mathrm{dm}}^{3}$ $=$ ${\left(1 \times {10}^{-} 1 \cdot m\right)}^{3}$ $=$ ${10}^{-} 3 \cdot {m}^{3} = 1 \cdot L$.

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

And $1 \cdot c {m}^{3} = {\left(1 \times {10}^{-} 2 m\right)}^{3}$ (because "c"-="centi, "10^-2), and thus,

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

$=$ $\frac{1}{1000} \times \frac{1}{1000} \cdot {m}^{3}$

But $\frac{1}{1000} \cdot {m}^{3} \equiv 1 \cdot L$

And $\frac{1}{1000} \cdot L \equiv 1 \cdot m L$, as required.

Confused yet?

I don't know what you mean by $G m$.

Dec 1, 2016

There is no conversion necessary. Litres and ${\mathrm{dm}}^{3}$ are numerically identical, as are $m l$ and $c {m}^{3}$.

#### Explanation:

${\mathrm{dm}}^{3}$ is "cubic decimetres". A decimetre is 10 cm - if you cube 10 cm you get 10 x 10 x 10 = 1000 $c {m}^{3}$ which is 1 litre.

$m l$ are millilitres or "thousandths of a litre". Therefore 1 $m l$ is the same as 1 $c {m}^{3}$