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Dilution factors tell us how many parts of each component of the mixture to mix together relative to each other. For example, a 10:1 dilution factor means that for every 1 part of the mix you add 10 parts of the diluting agent. The parts can be measured in grams, mLs, or any number of measurements, but for two liquids mLs would be the easiest. We are using the entire 2 mL of the broth culture and diluting it with water (since I am assuming that the broth is based on water). So we multiply the 2 mL by a factor of 10 to get 20 mL of water. So the correct procedure would be to take the entire 2 mL sample of the broth culture and add 20 mL of water to it to get a total volume of 22 mL of the diluted culture.
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