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."

2 Answers
May 13, 2017

Answer:

#"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.

May 13, 2017

Answer:

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.