A 16 lb dog is to get 16 mg/kg of a medication. How many mg does he recieve?

Question

A 16 lb dog is to get 16 mg/kg of a medication. How many mg does he receive? 

Answer 1

This is a problem regarding units. We know how many mg of medication is needed per kg, but not per pound. What we need to do, is to convert 16 lbs to kg, and then we will know how much medication is needed. There is a method of unit conversion that is quite nice when you write it out. Start by writing out the given values with the given units and then transform the units by multiplying by conversion factors. The idea is, conversions are set up so that the units that you want remain, while the units that you don't want cancel out. We do need some extra info here: 1 kg = 2.2 pounds. As a conversion factor, we can write this as (1kg/2.2 pounds) or (2.2 pounds/1 kg). Both of this equal 1, so multiplying by them won't change what the answer should be. Here's how it works. 16 mg/kg * (1 kg / 2.2 lbs) * 16 lbs = 116.4 mg. Notice that I used the 1kg/2.2 lbs conversion factor, since I wanted to cancel the kg in the bottom of the 16 mg/kg. Then I multiplied by the 16 lb, which is the weight of the dog, to cancel the lb unit. This leaves me with mg--which is the unit of the answer I wanted.

Answer 2

1 lb = 0.453592 kg

16 lb = 7.257472 kg

 

16 mg per 1 kg

116.119552 mg per 16 kg

 

The doe should receive 116 mg (on the safe side).