Okay I did the easy part first:A medicinal dosage is 5 milligrams per pound of bodyweight. The medicine is 0.9 grams per milliliter. If a patient is 72.7 kilograms, how many milliliters of dosage should the patient take?

5 mg / 1 lb = .005 g / 1 lb

Since there's .005 grams in 5 milligrams. Now I will change it to kilograms:

.005 g / 1 lb = x / 2.20462262 lb

Since there's 2.20462262 lbs. in 1 kg so I want the ratio set for grams per kilogram (since 1 kg is 2.20462262 lbs. and I need to keep the units in lbs)

Cross multiply:

.005 g / 1 lb = x / 2.20462262 lb

(2.20462262 lb)(.005 g) = (1 lb)(x)

Divide both sides by 1 lb which cancels out the lb. unit on both sides:

(2.20462262)(.005 g) = x

So:

0.0110231131 g = x

So I will need 0.0110231131 grams per 2.20462262 lbs. of body weight. 2.20462262 lbs is also 1 kg so I will just exchange the units:

0.0110231131 grams / 1 kg

The dosage is 0.0110231131 grams per 1 kg, so:

0.0110231131 grams / 1 kg = x / 72.7 kilograms

Cross multiply:

(1 kg)(x) = (0.0110231131 grams)(72.7 kilograms)

Divide both sides by 1 kg:

x = (0.0110231131 grams)(72.7)

x = 0.801380322 grams

So the patient needs 0.801380322 grams of medicine total for his bodyweight.

What I don't understand is what to do next. What does 0.9 grams per milliliter mean? I thought milliliter is a unit of volume. So that means there's 0.9 grams of medicine per 1 milliliter of volume (of maybe water or some other physical space, maybe like in pill form or otherwise), but what does that have to do with problem or anything at all?

I know I get the correct answer if I divide: 0.801380322 grams / (.9 grams / 1 mL)

But I don't understand the reason why.