Unit Conversions

Jan 2020
I'm trying to make my way through a multi-step unit conversion problem, but I'm seeming to get stuck half way through. It's not clicking in my head, and I don't know how to set up the problem that it's asking me to do.

Part 1 of the problem reads: Kathy, a 125 lb woman, wishes to take Miracle Drug to cure her cold. One dose of Miracle Drug is 6.0 mg of drug per kg of bodyweight (6.0 mg/kg or more specifically, 6.0 mg/kg/dose or 6.0 mg/kg-does). How much drug in mg should Kathy take for one dose?

This part of the problem I can understand. I took 125 lb, multiplied it by 1kg over 2.2046 lb, lb then cancels out and I'm left with kg on top. 125 divided by 2.2046 equals 56.6. So the answer is 125 lb is equal to 56.6 kg. To get one dose, I just multipled 6.0 mg times 56.6 kg, which equals 339.6 mg for one dose according to her weight in kg.

Part 2 of the problem is where I get stumped. It reads: If the concentration of Miracle Drug in the bottle Kathy found in her medicine cabinet is 26.0 mg of drug for every mL of solution (26.0 mg/mL), how many mL should she consume for one dose?

I can't quite understand what it is asking me. Is it asking me to convert mg to mL? I was told that it's just another simple unit conversion problem, but I still can't vision in my head how I should set it up. Can someone explain what it's asking of me so that I can figure out how to set up a unit conversion to solve it?
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Apr 2015
how many mL should she consume for one dose?
Firstly congratulations on posting sensibly explaining what you have done and what you can't do.
This should be a model for others to follow.

However I should point out that Chemists need to be more accurate in their calculations.
My caculator says that 125/2.2046 = 56.69963 ie 56.7 to 3sf.

So back to part 2

The question asks how many mL

and you are told that each mL contains 26.00 mg.

Coming back to your arithmetic, I make the required dose = 6 times 125/2.2046 = 340.1978 mg

So you see that you have reduced the significant figures too early and too far.

Since each mL contains 26.00 mg the required dose is 340.1978 / 26.00 = 13.0845 or 13.1 mL