# Why can't you just convert meters cubed to mL >> then >> convert mL to Liters? Giving: 0.019L (after Sig Figs)??﻿ This references the video "Converting Metric Units of Volume."

May 13, 2017

$\text{1 cubic metre}$ IS $1000 \cdot L$ or $1000 \cdot {\mathrm{dm}}^{3}$. I have not seen the video. And $18.8 \cdot {m}^{3} = 18.8 \times {10}^{3} \cdot L \ldots \ldots \ldots . .$

#### Explanation:

A cubic metre is a HUGE volume. And $1 \cdot c {m}^{3} \equiv 1 \cdot m L = {10}^{-} 3 \cdot L$. These are all common units of volume in the laboratory. In Europe, we buy milk in litres, and in England, sometimes we buy milk in $\text{pints}$, $600 \cdot m L$.

$1 \cdot c {m}^{3} = {\left(1 \times {10}^{-} 2 \cdot m\right)}^{3}$. Why? Because the prefix $\text{centi} \equiv {10}^{-} 2$. And thus............

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

Sometimes I remember that $1 \cdot {m}^{3}$ (which is a HUGE volume!), is $1000 \cdot L$, and that there are ${10}^{3} \cdot c {m}^{3}$ in a $L$. An equivalent term for the $\text{litre}$ is $\text{cubic decimeter}$, ${\mathrm{dm}}^{3}$.

And thus $1000 \cdot L = {10}^{3} \cdot L \times {10}^{-} 6 \cdot {m}^{3} = 1 \times {10}^{-} 3 \cdot {m}^{3}$.

Equivalently $1 \cdot L = 1 \cdot {\mathrm{dm}}^{3} = {\left(1 \times {10}^{-} 1 \cdot m\right)}^{3} = {10}^{-} 3 \cdot {m}^{3}$, as required.

May 13, 2017

There's no reason why you can't … if you know the conversion factors.

#### Explanation:

(By the way, the correct answer is 18 800 L.)

Do you know that the conversion is $\text{1 m"^3 = 10^6color(white)(l) "mL}$?

If so, you can write

18.8 color(red)(cancel(color(black)("m"^3))) × (10^6 color(red)(cancel(color(black)("mL"))))/(1 color(red)(cancel(color(black)("m"^3)))) × "1 L"/(10^3 color(red)(cancel(color(black)("mL")))) = "18 800 L"

However, that seems to me to be taking the long way around.

I would bet that more people remember the conversion, $\text{1 m"^3 = "1000 L}$.

They would write

18.8 color(red)(cancel(color(black)("m"^3))) × "1000 L"/(1 color(red)(cancel(color(black)("m"^3)))) = "18 800 L"

Both methods are equally valid.