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Surprising effects of small numbers: Why parts-per-notation is so important for environmental science?
In science and engineering, parts-per notation is a pseudo-unit used to describe small, usually dimensionless quantities such as mole fraction or mass fraction. These fractions are ratio measurements of quantities, so they are pure numbers and have no corresponding units. Common parts-per notation includes parts per million (ppm, 10−6), parts per billion (ppb, 10−9), parts per trillion (ppt, 10−12), and parts per trillion. (ppq, 10−15). Although these notations are not part of the International System of Units (SI), their use in environmental science and many other technical fields is widespread and important.
Parts-per-point notation is an effective method for describing the relative abundance of dissolved minerals or contaminants in dilute solutions.
In chemistry, parts-per notation is often used to describe dilution in a solution. For example, when we say that the concentration of a pollutant in water is "1 ppm", this means that there is one millionth of a gram of the pollutant per gram of water. In aqueous solutions, the density of water is often assumed to be 1.00 g/mL, an assumption that allows ppm to be easily converted to milligrams per liter (mg/L). Further, ppb usually corresponds to micrograms per liter (μg/L) and ppt corresponds to nanograms per liter (ng/L). This conversion method is of great importance in environmental science because concentrations of many environmental pollutants are usually detected and reported at low levels.
Parts-per notation also plays an important role in physics and engineering applications. For example, the coefficient of thermal expansion of a metal alloy can be expressed as "α = 1.2 ppm/°C", which means that its length will expand by 1.2 microns for every degree of Celsius increase. Such a representation is not only intuitive but also convenient for scientists to perform calculations and comparisons. In terms of measurement accuracy, for example when using a laser rangefinder for land surveying, its accuracy can be expressed as "accuracy = 1 ppm", which is crucial to improving the reliability of the measurement.
In mathematical expression, the quantity "2 nanometers per meter" is simplified to "2 ppb", showing the power of parts-per notation.
However, although parts-per notation is widely used in practice, there are still some theoretical controversies and criticisms. First, it is not an official SI unit. Although the International Bureau of Weights and Measures (BIPM) acknowledges its use, it still advises caution because different countries may have different definitions of "billion". This leads to some ambiguity in the application of ppb and ppt. Therefore, experts suggest that when using parts-per notation, its specific meaning should be clearly defined.
Alternatively, parts-per notation may correspond to mass fraction, mole fraction, or volume fraction. This often causes confusion in scientific communication, as no one necessarily specifies the quantities used. Therefore, users should prefer to indicate specific units (such as kg/kg, mol/mol, etc.) when using this notation. This uncertainty is particularly important in gas studies, where conversion factors between mass fractions and mole fractions may suddenly become apparent, which is crucial in analytical interpretation.
In some professional fields, although the use of parts-per notation is fixed, there may be inconsistencies in standards and usage between disciplines, which makes researchers undefined in publishing results, which can easily lead to misunderstandings.
To overcome this challenge, the scientific community has proposed SI-compatible alternative expressions. These expressions allow different disciplines to use standardized units to a certain extent, thereby improving the accuracy of communication. However, parts-per notation remains an indispensable tool in the field of technology, and its practicality cannot be ignored, especially in fields such as environmental monitoring and public health.
Ultimately, while parts-per notation is powerful for expressing small quantities with precision, there are concerns about ambiguity and confusion in its use. Should we promote the standardization of these expressions to better serve the development of scientific research and practice?
