If 1 ml of volume contains 1 mg of epinephrine, then 0.1 ml of volume contains 0.1 mg of epinephrine.
Let x be the number of ml you need.
Ratio: 1 ml is to 1 mg as x ml is to 0.1 mg
(1 ml)/(1 mg) = (x ml)/(0.1 mg)
Cross multiply.
1 * x = 1 * 0.1
x = 0.1
Answer: 0.1 ml
