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Math Help - Understanding Units

  1. #1
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    Understanding Units

    Please advise if you can

    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
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  2. #2
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    Quote Originally Posted by David Green View Post
    Please advise if you can

    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

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