Dilution Mathematics

Flo89

Hi Guys,

I've been told in work that 0.5mg/ml equates to 500mg/µL ...but that can't be, can it?

There's an equation that we have to use to work out the volume of sample required make up a certain amount (A mg/µL (divided by) B mg/µL *(multiplied by) C µL = D µL).

Because the mg cancel each other out, it's not really important what units they're in because the end figure will work out correct. However, I can't get my head around it. They've divided the unit ml by 1000 to go to µL and multiplied the top by 1000 to balance it...but that doesn't balance it! Surely it should be 0.0005 mg/µL?? Like if I have 5 apples in one box and then decide to divide the box into 5 pieces, I don't suddenly have 25 apples per piece!! Like I said, the end figure works out correctly but still...

Any opinions on the matter would be highly appreciated.

A Disgruntled Employee

Victor

Why are mixed units being used? It is the source of much error and quite possibly misdosage, potentially with serious results.

1 µL = 1 Microlitre = 0.000001 Litres
1 ml = 1 millilitre = 0.001 Litres

0.5mg/ml = 0.5g/l (multiplying both sides by 1000) approximating a fraction of a sugar cube per litre

500mg/µl = 0.5g/µl (no change) = 500g/ml (multiplying both sides by 1000) = 500kg/l (multiplying both sides by a further 1000) which is pretty much impossible - I imagine it approximates the density in the middle of a star.

This is out by a factor of 1 million. Someone is wrong. Check to make sure it isn't you.

Yakuza

Quite right, the second dosage has the numerator 1000 times (500 vs 0.5) larger than that of the first, and the denominator 1000 times smaller than that of the first (microlitres vs millilitres), or as Victor says, the second dosage is out by a factor of 1000 / (1/1000) --> 1000000.

locum-motion

Both other replies are correct.
Either you misunderstood what you were told, or the person who told you misunderstood what they were telling you!