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In order to convert between milligrams and micromoles, one has to know the molar mass of the substance in question, then simply convert from grams to moles. As an example, let's assume that the measurement is that of oxygen, or O2, and that there's 10 milligrams per liter. First, divide by 1,000, to convert to grams, in this case, .01 grams. Then, divide this amount by the molar mass, which represents the number of grams in a mole. For O2, this is approximately 31.9988. This gives us a result of around .0003125 moles, or 3.125 x 10^-4. Then, we multiply by 1,000,000 to convert from moles to micromoles. The end result is approximately 312.5 micromoles in the liter.

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