# Understanding Units

• Feb 21st 2011, 11:50 AM
David Green
Understanding Units

I have one litre of liquid, this is equal to 1000 ml. I want to add 25% more liquid to the original volume.

I say 25% / 100 x 1000 = 250 ml. I then add this to the original 1000 ml to give 1250 ml, then I say; 1250 ml / 1000 ml = 1.25 L

The maths looks good, but the problem for me is in the units, you see if ml / ml is cancelled out, then I know its a fluid, but where does the L litre come from if I have cancelled the units out?

I thought that would leave unity?

David
• Feb 21st 2011, 12:21 PM
TheEmptySet
Quote:

Originally Posted by David Green

I have one litre of liquid, this is equal to 1000 ml. I want to add 25% more liquid to the original volume.

I say 25% / 100 x 1000 = 250 ml. I then add this to the original 1000 ml to give 1250 ml, then I say; 1250 ml / 1000 ml = 1.25 L

The maths looks good, but the problem for me is in the units, you see if ml / ml is cancelled out, then I know its a fluid, but where does the L litre come from if I have cancelled the units out?

I thought that would leave unity?

David

You must take care with your unit fractions what you really have is

$\displaystyle 1000 \text{mL}=1\text{L} \iff \frac{1\text{L}}{1000 \text{mL}}$

So when you multiply by this fraction the mL reduce out, but the L stays in the numerator.

This gives

$\displaystyle \displaystyle 1250\text{mL}\left( \frac{1\text{L}}{1000 \text{mL}}\right)=1.25\text{L}$