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Because the density of a dilute aqueous solution is close to 1.00 g/mL, we frequently equate 1 g of water with 1 mL of water, although this equivalence is only approximate. Therefore, 1 ppm corresponds to 1 µg/mL ( 1 mg/L) and 1 ppb is 1 ng/mL ( 1 g/L). I do not understand where they are getting those micrometer and nanometer measurements..

Chemistry
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I think ppm and ppb is indicate how it's concentrate but not affect itself density of matter, ppm can indicate any substance such as have 1g of NaCl in 10^6 ml solution, the density of NaCl still constant
remind that ppm ppb molar or molal is concentration or molar density but density is mass density (ppm or ppb can be report as mass density as well) things that make you confuse, may be cause of its unit is similar >> mass/volume
1 ppm = \(10^{-6}\) = \(\Large \frac {10^{-6}g}{1g}\)=\(\Large \frac {1\mu g}{1g}\), which corresponds in water to: \(\Large \frac {1\mu g}{1mL}\) = \(\Large \frac {1mg}{1L}\)

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