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"1mg of substance equals 3IU. "
An IU has NO milligram, microgram, gram, etc. equality. An IU is an International Unit, which is a measurement of ACTIVITY, not true weight/mass. An IU is determined by an international commitee of scientists who wish to standardize biological compounds, such as vitamins (A, E, D, etc.), hormones (insulin, gh - growth hormone (somatropin) - , etc.).
So in the case of gh - growth hormone (somatropin) - , 1mg DOES equal 3IU's, but this is not the case for any other compound, such as beta-carotene, which is something like 6.25mg equals 1,000 IU's.
Also, IU's cannot be equated to a volume, since this is arbitrary. The IU's/ml is determined by the person who makes the solution.