For both small and large concentrations, parts-per notation is a very convenient way to communicate numbers that would ordinarily have many zeros (either before or after a decimal point). For example, 3 ppt (parts per trillion) is much cleaner than reporting 0.000000000003. Additionally, it is important to distinguish what units are being described. Is it 3 particles per trillion particles? 3 grams per trillion grams? In other words, parts-per notation offers a unit-less ratio, and in scientific literature the true units are either directly stated or implied from context. The most frequently used notations are parts per million (ppm) or parts per billion (ppb).
Parts per million measures a small amount of something compared to a million of the substance it is dissolved in. For example, 18 ppm of sugar in water by weight means that, if there were a million grams of that water, there would be 18 grams of sugar in it. This standard is especially useful in computing water quality, as the measurement of minerals or impurities in a sample can be extrapolated to whatever size of water of interest. For context of this size, 1 ppm is approximately 4 drops of ink in 55 gallons, or 1 inch in 16 miles. One ppm is equivalent to 1 milligram per liter.
Parts per billion is the smallest dimension generally used. It references an amount of something compared to a billion of the substance it is within. For context, 1 ppb is approximately the width of 1 human hair in 68 miles, or 1 second per 32 years. One ppb is equivalent to 1 microgram per liter.