Similarly, parts-per notation is used also in physics and engineering to express the value of various proportional phenomena. For instance, a special metal alloy might expand 1.2 micrometers per meter of length for every degree Celsius and this would be expressed as "α = 1.2 ppm/°C." Parts-per notation is also employed to denote the change, stability, or uncertainty in measurements. For instance, the accuracy of land-survey distance measurements when using a laser rangefinder might be 1 millimeter per kilometer of distance; this could be expressed as "Accuracy = 1 ppm.
The above parts-per notations are all dimensionless quantities; that is, in mathematical expressions, the units of measurement always cancel in fractions like "2 nanometers per meter" (2 n
m/ m = 2 nano = 2 × 10–9 = 2 ppb = 2 × 0.000000001) so the quotients are pure-number coefficients with values less than 1. When parts-per notations, including the percent symbol (%), are used in regular prose (as opposed to mathematical expressions), they are still pure-number dimensionless quantities, however, they generally take the literal "parts per" meaning of a comparative ratio (e.g., "2 ppb" would generally be interpreted as "two parts in a billion parts").
Note that although the International Bureau of Weights and Measures (an international standards organization known also by its French-language initials BIPM) recognizes the use of parts-per notation, it is not formally part of the International System of Units (SI). Consequently, according to IUPAP, "a continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt." Also, because the named numbers starting with a "billion" have different values in different countries, the BIPM suggests avoiding the use of "ppb" and "ppt" to prevent misunderstanding. Nevertheless, parts-per notation, particularly the expression "ppm", remains widely used in technical disciplines because of its convenience in denoting dimensionless quantities. See Alternatives to parts-per notation, below.
For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that the two systems were often referred to as "British" and "American" usage respectively. Today, the UK uses the short scale exclusively in official and mass media usage and, although some long-scale usage still continues, the terms "British" and "American" no longer reflect usage. See also Long and short scales. However, the long scale is dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. See also Names of large numbers.
Although the BIPM recognizes the use of "parts per million" (ppm) to represent dimensionless quantities, it cautions that due to the above-mentioned language differences and also because "ppt" occasionally means "parts per thousand," both "ppb" and "ppt" should be avoided to prevent misunderstanding. Clearly, this admonition would also apply to "parts per quadrillion" (ppq) for the same language-based reason. The U.S. National Institute of Standards and Technology (NIST) takes a more stringent position, stating that "the language-dependent terms 'part per million,' 'part per billion,' and 'part per trillion'…are not acceptable for use with the SI to express the values of quantities." Note however, that the NIST's stated premise for its position is only partially true; "million" has only one meaning in all languages. Note too, that although "percent" (%) is not formally part of the SI, both the BIPM and the ISO, take the position that "in mathematical expressions, the internationally recognized symbol % (percent) may be used with the SI to represent the number 0.01" for dimensionless quantities.
Because parts-per notation generally has a well-understood meaning in modern, English-speaking scientific circles, and because its use simplifies the expression of dimensionless quantities, parts-per notation remains widely used in technical disciplines today. Expressions that the BIPM does not explicitly recognize as being suitable for denoting dimensionless quantities with the SI are shown in underlined green text text in the chart below.
|NOTATIONS FOR DIMENSIONLESS QUANTITIES|
|A strain of…||2 c||2 parts per hundred||2%||2 × 10–2|
|A sensitivity of…||2 mV/V||2 parts per thousand||2 ‰||2 × 10–3|
|A sensitivity of…||0.2 mV/V||2 parts per ten thousand||2 ‱||2 × 10–4|
|A sensitivity of…||2 µV/V||2 parts per million||2 ppm||2 × 10–6|
|A sensitivity of…||2 nV/V||2 parts per billion||2 ppb||2 × 10–9|
|A sensitivity of…||2 pV/V||2 parts per trillion||2 ppt||2 × 10–12|
|A mass concentration of…||2 mg/kg||2 parts per million||2 ppm||2 × 10–6|
|A mass concentration of…||2 µg/kg||2 parts per billion||2 ppb||2 × 10–9|
|A mass concentration of…||2 ng/kg||2 parts per trillion||2 ppt||2 × 10–12|
|A mass concentration of…||2 pg/kg||2 parts per quadrillion||2 ppq||2 × 10–15|
|A stability of…||1 (µA/A)/min.||1 part per million per min.||1 ppm/min.||1 × 10–6/min.|
|A change of…||5 nΩ/Ω||5 parts per billion||5 ppb||5 × 10–9|
|An uncertainty of…||9 µg/kg||9 parts per billion||9 ppb||9 × 10–9|
|A shift of…||1 nm/m||1 part per billion||1 ppb||1 × 10–9|
|A strain of…||1 µm/m||1 part per million||1 ppm||1 × 10–6|
|A temperature coefficient of…||0.3 (µHz/Hz)/°C||0.3 part per million per °C||0.3 ppm/°C||0.3 × 10–6/°C|
|A frequency change of…||0.35 × 10–9 ƒ||0.35 part per billion||0.35 ppb||0.35 × 10–9|
Note that the notations in the "SI units" column above are all dimensionless quantities; that is, the units of measurement cancel in expressions like "1 nm/m" (1 n
m/ m = 1 nano = 1 × 10–9) so the quotients are pure-number coefficients with values less than 1.
Common parts-per notations in terms of the uno are given in the table below.
|IUPAP'S "UNO" PROPOSAL|
|10–2||2%||2 centiuno||2 cU||2 × 10–2|
|10–3||2 ‰||2 milliuno||2 mU||2 × 10–3|
|10–6||2 ppm||2 microuno||2 µU||2 × 10–6|
|10–9||2 ppb||2 nanouno||2 nU||2 × 10–9|
|10–12||2 ppt||2 picouno||2 pU||2 × 10–12|
In 2004, a report to the International Committee for Weights and Measures (known also by its French-language initials CIPM) stated that response to the proposal of the uno "had been almost entirely negative" and the principal proponent "recommended dropping the idea." To date, the uno has not been adopted by any standards organization and it appears unlikely it will ever become an officially sanctioned way to express low-value (high-ratio) dimensionless quantities. The proposal was instructive, however, as to the perceived shortcomings of the current options for denoting dimensionless quantities.
Note however, that it is not uncommon to express aqueous concentrations—particularly in drinking-water reports intended for the general public—using parts-per notation (2.1 ppm, 0.8 ppb, etc.) and further, for those reports to state that the notations denote milligrams per liter or micrograms per liter. Whereas "2.1 mg/L" is technically not a dimensionless quantity on the face of it, it is well understood in scientific circles that one liter of water has a mass of one kilogram and that "2.1 mg/kg" (2.1 ppm) is the true measure. The goal in all technical writing (including drinking-water reports for the general public) is to clearly communicate to the intended audience with minimal confusion. Drinking water is intuitively a volumetric quantity in the public's mind so measures of contamination expressed on a per-liter basis are considered to be easier to grasp.