Question

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."

Answer 1

`"1 cubic metre"` IS `1000*L` or `1000*dm^3`. I have not seen the video. And `18.8*m^3=18.8xx10^3*L...........`

Explanation:

A cubic metre is a HUGE volume. And `1*cm^3-=1*mL=10^-3*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 `"pints"`, `600*mL`.

`1*cm^3=(1xx10^-2*m)^3`. Why? Because the prefix `"centi"-=10^-2`. And thus............

`1*cm^3=(1xx10^-2*m)^3=1xx10^-6*m^3`.

Sometimes I remember that `1*m^3` (which is a HUGE volume!), is `1000*L`, and that there are `10^3*cm^3` in a `L`. An equivalent term for the `"litre"` is `"cubic decimeter"`, `dm^3`.

And thus `1000*L=10^3*Lxx10^-6*m^3=1xx10^-3*m^3`.

Equivalently `1*L=1*dm^3=(1xx10^-1*m)^3=10^-3*m^3`, as required.

It is worthwhile getting your head around these problems. If there is an issue you want further clarified ask away, and someone will help you.

Answer 2

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 `"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, `"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.