Parts-per notation: Difference between revisions

{{Short description|Set of pseudo units to describe small values of miscellaneous dimensionless quantities}}

{{Redirect|Parts per billion|the film|Parts per Billion{{!}}''Parts per Billion''}}

At 1  ppm the solution is a very pale yellow. As the concentration increases the colour becomes a more vibrant yellow, then orange, with the final 10,000  ppm a deep red colour.]]

==Overview Applications ==

Parts-per notation is often used describing dilute solutions in [[chemistry]], for instance, the relative abundance of dissolved minerals or pollutants in [[water]]. The quantity "1 ppm" can be used for a mass fraction if a water-borne pollutant is present at one-millionth of a [[gram]] per gram of sample solution. When working with [[aqueous solutionssolution]]s, it is common to assume that the density of water is 1.00  g/mL. Therefore, it is common to equate 1  kilogram of water with 1 L of water. Consequently, 1  ppm corresponds to 1 mg/L and 1 ppb corresponds to 1 μg/L.

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&nbsp;[[micrometre|micrometers]] per [[metre|meter]] of length for every [[Celsius|degree Celsius]] and this would be expressed as {{nobr|"''[[coefficient of thermal expansion|{{mvar|α}}]]''&nbsp; {{=&nbsp;}} 1.2&nbsp; ppm/°C".}} Parts-per notation is also employed to denote the change, stability, or [[standard deviation|uncertainty]] in measurements. For instance, the accuracy of land-survey distance measurements when using a [[laser rangefinder]] might be 1&nbsp;millimeter per kilometer of distance; this could be expressed as "[[Accuracy and precision|Accuracy]]&nbsp;=&nbsp;1&nbsp;ppm."<ref>{{efn|
This is a simplified explanation. Laser rangefinders typically have a measurement [["granularity]]" of one to ten millimeters; thus, the complete specification for distance measurement accuracy might read as follows:&nbsp; "Accuracy: {{nobr|±(1&nbsp; mm&nbsp; +&nbsp; 1&nbsp; ppm)".}} Consequently, a distance measurement of only a few meters would still have an accuracy of ±1&nbsp;mm in this example.</ref>

Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. In fractions like "2&nbsp;nanometers per meter" {{nobr|(2&nbsp; n <s>m</s> / <s>m</s>&nbsp; {{=}} 2&nbsp; nano&nbsp; {{=}} 2&nbsp;×&nbsp;2×{{10^{^|−9}&nbsp;}} {{=}} 2&nbsp; ppb&nbsp; {{=}} 2&nbsp; ×&nbsp; {{val|0.000,000,001}}),}} so the [[quotient]]s are pure-number [[coefficient]]s with positive values less than or equal to&nbsp;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&nbsp;ppb" would generally be interpreted as "two parts in a billion parts").<ref name="BIPM">{{cite web |title=Stating values of dimensionless quantities, or quantities of dimension one |at=§&nbsp;5.3.7 |website=BIPM: [|url=http://www.bipm.org/en/publications/si-brochure/section5-3-7.html 5.3.7 ''Stating values of dimensionless quantities, or quantities of dimension one]''].}}</ref>

Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the [[coefficient of thermal expansion|expansion coefficient]] of a certainsome [[brass]] alloy, ''{{nobr|[[coefficient of thermal expansion|{{mvar|α''&nbsp;}}]] {{=&nbsp;}} 18.7&nbsp; ppm/°C,}} may be expressed as 18.7&nbsp;([[micrometre|μm]]/[[meter|m]])/°C, or as 18.7&nbsp;(μ [[inch|in]]/[[inch|in]])/°C; the numeric value representing a relative proportion does not change with the adoption of a different unit of length.<ref>{{efn|
In the particular case of coefficient of thermal expansion, the change to inches (one of the [[United States customary units|U.S. customary units]]) is typically also accompanied by a change to [[Fahrenheit|degrees Fahrenheit]]. Since a Fahrenheit-sized interval of temperature is only 5/{{sfrac| 5 |9}} that of a Celsius-sized interval, the value is typically expressed as {{nobr|10.4&nbsp; (μinμ [[inch|in]]/[[inch|in]])/°F}} rather than {{nobr|18.7&nbsp; (μinμ [[inch|in]]/[[inch|in]])/°C.</ref> }}
}}
Similarly, a [[metering pump]] that injects a trace chemical into the main process line at the proportional flow rate ''{{nobr|[[volumetric flow rate|{{mvar|Q}}]]<{{sub>|p</sub>''&nbsp;}} {{=&nbsp;125&nbsp;}} 12 ppm,}} is doing so at a rate that may be expressed in a variety of volumetric units, including {{nobr|125&nbsp;μL μ[[litre|L]]/[[litre|L]],}} {{nobr|125&nbsp; μ [[Gallon|gal]] / [[Gallon|gal]],}} 125&nbsp;cm³/[[cubic metre|m³]], etc.

!per<br />1,000mille<br />(‰)

*''One part per [[100 (number)|hundred]]'' is generally represented by the [[percent sign]] (%) and denotes [[percentage|one part per 100 ({{10^|2}}) parts]], and a value of {{10^|-2}}. This is equivalent to about fifteenfourteen minutes out of one day.

*''One part per [[1000 (number)|thousand]]'' should generally be spelled out in full and '''not''' as "ppt" (which is usually understood to represent "parts per [[trillion (short scale)|trillion]]"). It may also be denoted by the [[per mille|permille]] sign (‰). Note however, that specific disciplines such as oceanography, as well as educational exercises, do use the "ppt" abbreviation. "One part per thousand" denotes one part per 1,000 ({{10^|3}}) parts, and a value of {{10^|-3}}. This is equivalent to about one and a halfninety minutesseconds out of one day.

*''One part per [[ten thousand]]'' is denoted by the [[permyriad]] sign (‱). Although rarely used in science (ppm is typically used instead), one permyriad has an unambiguous value of one part per 10,000 ({{10^|4}}) parts, and a value of {{10^|-4}}. This is equivalent to about nine seconds out of one day. <br/>In contrast, in [[finance]], the [[basis point]] is typically used to denote changes in or differences between percentage interest rates (although it can also be used in other cases where it is desirable to express quantities in hundredths of a percent). For instance, a change in an interest rate from 5.15% per annum to 5.35% per annum could be denoted as a change of 20 basis points (per annum).<!--NOTE TO EDITORS:

--> As with interest rates, the words "per annum" (or "per year") are often omitted. In that case, the basis point is a quantity with a dimension of (time⁻¹).<ref>{{citeCite web |url=https://corporatefinanceinstitute.com/resources/knowledge/financefixed-income/basis-points-bps-definition/|title=What are Basis Points (BPS)?|website=Corporate Finance Institute}}</ref>

* ''One part per [[100,000|hundred thousand]]'', ''[[per cent mille]]'' ('''pcm''') or ''milli-percent'' denotes one part per 100,000 ({{10^|5}}) parts, and a value of {{10^|-5}}. It is commonly used in [[epidemiology]] for mortality, crime and disease prevalence rates, and nuclear reactor engineering as a unit of reactivity. In [[time measurement]] it is equivalent to about 5 minutes out of a year; in [[distance measurement]], it is equivalent to 1&nbsp;cm of error per km of distance traversed.

* ''One part per [[1,000,000|million]]'' ('''ppm''') denotes one part per 1,000,000 ({{10^|6}}) parts, and a value of {{10^|-6}}. It is equivalent to about 32 seconds out of a year or 1 mm of error per km of distance traversed. In [[mining]], it is also equivalent to one [[gram]] per [[metric ton]], expressed as g/t.

* ''One part per [[1000000000 (number)1,000,000,000|billion]]'' ('''ppb''') denotes one part per 1,000,000,000 ({{10^|9}}) parts, and a value of {{10^|-9}}. This is equivalent to about three seconds out of a [[century]].

Although the [[International Bureau of Weights and Measures]] (an international standards organization known also by its [[France|French]]-language initials BIPM) recognizes the use of parts-per notation, it is not formally part of the [[International System of Units]] (SI).<ref name="BIPM" /> Note that although "[[Percentage|percent]]" (%) is not formally part of the SI, both the BIPM and the [[International Organization for Standardization]] (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.<ref name="BIPM" /><ref>''Quantities and units''. Part 0: ''General principles'', ISO 31-0:1992.</ref> According to [[International Union of Pure and Applied Physics|IUPAP]], ''"a continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt"''.<ref name="IUPAP">{{cite web |title=Report on Recent Committee Activities on Behalf of IUPAP to the 1999 IUPAP General Assembly |first=Brian W. |last=Petley |date=September 1998 |url=http://archive.iupap.org/commissions/interunion/iu14/ga-99.html |access-date=2017-08-15 |url-status=live |archive-url=https://web.archive.org/web/20170815113700/http://archive.iupap.org/commissions/interunion/iu14/ga-99.html |archive-date=2017-08-15}}</ref> Although [[#SI-compliant expressions|SI-compliant expressions]] should be used as an alternative, the parts-per notation remains nevertheless widely used in technical disciplines. The main problems with the parts-per notation are set out below.

Because the [[names of large numbers|named numbers]] starting with a "[[Long and short scales|billion]]" have different values in different countries, the BIPM suggests avoiding the use of "ppb" and "ppt" to prevent misunderstanding. The U.S. [[National Institute of Standards and Technology]] (NIST) takes the stringent position, stating that ''"the language-dependent terms [...] are not acceptable for use with the SI to express the values of quantities"''.<ref>NIST: ''[http://physics.nist.gov/Pubs/SP811/sec07.html#7.10.3 Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt]''.</ref>

To distinguish the mass fraction from volume fraction or mole fraction, the letter "w" (standing for "weight") is sometimes added to the abbreviation (e.g. ppmw, ppbw).<ref>{{cite web |title=Units |series=Introduction to Greengreen Engineeringengineering |date=2012-08-23 |df=dmy-all |publisher=[[University of Virginia]] |url=https://pages.shanti.virginia.edu/CE_2050_F12/2012/08/23/units/}}</ref>

The usage of the parts-per notation is generally quite fixed insidewithin mosteach specific branchesbranch of science, but often in a way that is inconsistent with its usage in other branches, leading some researchers to draw the conclusionassume that their own usage (mass/mass, mol/mol, volume/volume, mass/volume, or others) is thecorrect onlyand correctthat oneother usages are incorrect. This, inassumption turn,sometimes leads them to not specify the details of their own usage in their publications, and others may therefore misinterpret their results. For example, [[electrochemistry|electrochemists]] often use volume/volume, while [[Chemical engineering|chemical engineers]] may use mass/mass as well as volume/volume, while [[chemist]]s, the field of [[occupational safety]] and the field of [[permissible exposure limit]] (e.g. permitted [[gas]] exposure limit in [[air]]) may use mass/volume. Unfortunatelly, Manymany academic publications of otherwise excellent level fail to specify their usageuse of the parts-per notation, which irritates some readers, especially those who are not experts in the particular fields in those publications, because parts-per-notation, without specifying what it stands for, can mean anything.{{Citation needed|date=October 2021}}

|align="center"|2&nbsp;μg/kg<!--NOTE TO EDITORS: SI convention is to use the base unit kilogram in formulas and equalities. However, whenever an SI prefix, like milli (m) or micro (m or µμ), is used with the unit of mass, the unit gram (symbol g) is used. This results in a mix of units, such as mg (a thousandth of a gram) over a kilogram (a thousand grams). Thus, one microgram divided by one kilogram is one ppb.-->

Note that the notations in the "SI units" column above are allfor the most part [[Dimensionless quantity|dimensionless quantities]]; that is, the units of measurement factor out in expressions like "1&nbsp;nm/m" (1&nbsp;n<s>m</s>/<s>m</s>&nbsp;= 1&nbsp;nano&nbsp;= 1&nbsp;×&nbsp;10⁻⁹) so the [[quotientratio]]s are pure-number [[coefficient]]s with values less than 1.

Because of the cumbersome nature of expressing certain dimensionless quantities per SI guidelines, the [[International Union of Pure and Applied Physics]] (IUPAP) in 1999 proposed the adoption of the special name "uno" (symbol: U) to represent the number 1 in dimensionless quantities.<ref name="IUPAP" /> In 2004, a report to the [[International Committee for Weights and Measures]] (CIPM) stated that the response to the proposal of the uno "had been almost entirely negative", and the principal proponent "recommended dropping the idea".<ref>{{cite web |title=Report of the 16th meeting (13–14 May 2004) to the International Committee for Weights and Measures, of the International Bureau of Weights and Measures |author=Consultative Committee for Units |date=13–14 May 2004 |url=http://www.bipm.org/utils/common/pdf/CCU16.pdf |url-status=dead |archive-url=https://web.archive.org/web/20140310054340/http://www.bipm.org/utils/common/pdf/CCU16.pdf |archive-date=2014-03-10}}</ref> To date, the uno has not been adopted by any [[standards organization]], and it appears unlikely that it will ever become an officially sanctioned way to express low-value (high-ratio) dimensionless quantities.

* [https://www.nist.gov/ National Institute of Standards and Technology] (NIST): [https://www.nist.gov/ Home page]

* [https://www.bipm.org/en/ International Bureau of Weights and Measures] (BIPM): [http://www.bipm.org/en/home/ Home page]