Liters is for volume, centimeters is for length. They don't convert.
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.001 liters (1 mL) is equal to one cubic centimeter.
To convert grams per cubic centimeter (g/cm^3) to milligrams per liter (mg/L), you need to multiply by 1000. This is because there are 1000 milligrams in a gram and 1000 cubic centimeters in a liter.
1000 ml = 1 liter, so 1 ml = .001 liters.
There are 1000 cubic centimeters (cc) in 1 liter.
1 liter = 1,000 milliliters = 1,000 cubic centimeters.