View source for Parts-per notation



==Overview==
[[Image:Image-Olympic Pool Munich 1972, color adj.jpg|thumb|right|307px|One part per trillion (1 ppt) is a proportion equivalent to one-twentieth of a drop of water diluted into a two-meter-deep, Olympic-size swimming pool.]]
'''“Parts-per” notation'''  is used, especially in [[science]] and [[engineering]], to denote [[Proportionality (mathematics)|relative proportions]] in measured quantities; particularly in low-value (high-ratio) proportions at the parts-per-million ('''ppm'''), parts-per-billion ('''ppb'''), and parts-per-trillion ('''ppt''') level. Since parts-per notations are quantity-per-quantity measures, they are known as ''[[Dimensionless quantity|dimensionless quantities]];'' that is, they are pure numbers with no associated [[units of measurement]]. In regular prose, parts-per notations generally take the literal “parts per” meaning of a comparative ratio. However, in mathematical expressions, parts-per notations function as [[coefficient]]s with values less than&nbsp;1.

==Overview==
Parts-per notation is often used in the measure of dilutions ([[concentration]]s) in [[chemistry]]; for instance, for measuring the relative abundance of dissolved minerals or pollutants in water. The expression “1&nbsp;ppm” means a given property exists at a relative proportion of one part per million parts examined, as would occur if a water-borne pollutant was present at a concentration of one-millionth of a [[gram]] per gram of sample solution.

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 [[micrometre|micrometers]] per [[metre|meter]] of length for every [[Celsius|degree Celsius]] and this would be expressed as “''[[Coefficient of thermal expansion|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 range-finder|laser rangefinder]] might be 1&nbsp;[[Millimetre|mm]] per [[Kilometre|km]] of distance; this could be expressed as “[[Accuracy and precision|Accuracy]]&nbsp;=&nbsp;1&nbsp;ppm.”<ref>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; <font face="courier, monaco, times new roman">Accuracy: ±(1&nbsp;mm&nbsp;+&nbsp;1&nbsp;ppm)</font>. Consequently, a distance measurement of only a few meters would still have an accuracy of ±1&nbsp;mm in this example.<sub>&nbsp;</sub></ref>

The above parts-per notations are all [[Dimensionless quantity|dimensionless quantities]]; that is, in mathematical expressions, the units of measurement always cancel in fractions like “2 nanometers per meter” (2&nbsp;n<strike>m</strike>/<strike>m</strike>&nbsp;= 2&nbsp;nano&nbsp;= 2&nbsp;×&nbsp;10<sup>–9</sup>&nbsp;= 2&nbsp;ppb&nbsp;= 2&nbsp;×&nbsp;0.000<span style="margin-left:0.2em">000<span style="margin-left:0.2em">001)</span></span> so the [[quotient]]s are pure-number [[coefficient]]s with values less than&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">BIPM: [http://www.bipm.org/en/si/si_brochure/chapter5/5-3-7.html 5.3.7 ''Stating values of dimensionless quantities, or quantities of dimension one]''<sub>&nbsp;</sub></ref>

Note that 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"/> Consequently, 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.”''<span style="margin-left:0.3em"><ref name="IUPAP">Report to the 1999 IUPAP General Assembly: ''[http://www.iupap.org/commissions/interunion/iu14/ga-99.html Report on recent Committee activities on behalf of IUPAP by Brian W Petley September 1998]<sub>&nbsp;</sub></ref></span> Also, because the [[Names of large numbers|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|Alternatives to parts-per notation]]'', below.

==Parts-per expressions==<!-- This specific section is linked from [[Uranium]] and other articles; please do not rename this section. In the following equivalencies, it is assumed tht one drop of water has a volume of 0.05 ml (20 drops per milliliter).-->
*''One part per [[Orders_of_magnitude_%28numbers%29#102|hundred]]'': Should be represented by the [[Percentage|percent]] (%) symbol and denotes one part per 100 parts, one part in 10<sup>2</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–2</sup>. This is equivalent to one drop of water diluted into 5 [[Litre|milliliters]] (one spoon-full) or one second of time in 1⅔ minutes.
*''One part per [[Orders_of_magnitude_%28numbers%29#103|thousand]]'': Should be spelled out in full and should avoid the use the “ppt” abbreviation, which is occasionally understood to represent “parts per trillion”. It may also be denoted by the [[permille]] (‰) symbol. Note however, that specific disciplines such as the analysis of ocean water salt concentration and educational exercises occasionally use the “ppt” abbreviation. “One part per thousand” denotes one part per 1000 parts, one part in 10<sup>3</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–3</sup>. This is equivalent to one drop of water diluted into 50 milliliters (ten spoon-fulls), or one second of time in 16⅔ minutes.
*''One part per [[Orders_of_magnitude_%28numbers%29#104|ten thousand]]'': Is denoted by the permyriad (‱) symbol. It is used almost exclusively in [[finance]], where it is known as the [[basis point]] and is typically used to denote fractional changes in percentages. For instance, a change in an interest rate from 5.15% to 5.35% would be denoted as a change of 20 basis points or 20&nbsp;‱.<!--NOTE TO EDITORS:

Unlike the % symbol, which constitutes a formatting exception to the rule of the SI, a space goes between the value and both the permille and permyriad symbols (‰ and ‱). Besides adhering to the rule of the SI, this is also good technical writing practice as it helps to distinguish these two, less-common symbols from the percent symbol so as to avoid confusion.

--> Although rarely used in science (ppm is typically used instead), one permyriad has an unambiguous value of one part per 10,000 parts, one part in 10<sup>4</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–4</sup>. This is equivalent to one drop of water diluted into half a [[Litre|liter]], or one second of time in approximately 2¾ hours.
*''One part per [[Orders_of_magnitude_%28numbers%29#106|million]]'' ('''ppm'''): Denotes one part per 1,000,000 parts, one part in 10<sup>6</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–6</sup>. This is equivalent to one drop of water diluted into 50 liters (roughly the fuel tank capacity of a compact car), or one second of time in approximately 11½ days.
*''One part per [[Orders_of_magnitude_%28numbers%29#109|billion]]'' ('''ppb'''): Denotes one part per 1,000,000,000 parts, one part in 10<sup>9</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–9</sup>. This is equivalent to 1 drop of water diluted into 250 [[44-gallon drum|chemical drums]] (50&nbsp;m³), or one second of time in approximately 31.7 years.
*''One part per [[Orders_of_magnitude_%28numbers%29#1012|trillion]]'' ('''ppt'''): Denotes one part per 1,000,000,000,000 parts, one part in 10<sup>12</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–12</sup>. This is equivalent to 1 drop of water diluted into 20, two-meter-deep [[Olympic-size swimming pool]]s (50,000&nbsp;m³), or one second of time in approximately 31,700 years.
*''One part per [[Orders_of_magnitude_%28numbers%29#1015|quadrillion]]'' ('''ppq'''): Denotes one part per 1,000,000,000,000,000 parts, one part in 10<sup>15</sup>, and a value of 1&nbsp;×&nbsp;10<sup>–15</sup>. This is equivalent to 1 drop of water diluted into a cube of water measuring approximately 368 meters on a side (fifty million cubic meters, which is a cube about as tall as the roof of the [[Empire State Building]]), or one second of time in approximately 31.7 million years. Although relatively uncommon in analytic chemistry, measurements at the ppq level ''are'' performed.<ref>The measurement of environmental toxins that have hormone-like, biological effects (e.g., [[phthalates]]) are commonly performed at the ppq level. Measurements of [[dioxin]] are routinely made at the ''sub''-ppq level. The [[United States Environmental Protection Agency|U.S. EPA]] currently sets a hard limit of 30&nbsp;ppq for dioxin in drinking water but once recommended a voluntary limit of 0.013&nbsp;ppq. Also, radioactive contaminants in drinking water, which are quantified by measuring their radiation, are often reported in terms of ppq. The ability to chemically detect contaminants at this level is truly an impressive feat; 0.013&nbsp;ppq is equivalent to the thickness of a sheet of paper versus a journey of 146,000 trips around the world.<sub>&nbsp;</sub></ref> <!-- EDITORS NOTE REGARDING 146,000 TRIPS AROUND THE WORLD:

The analogy of paper thickness vs. 146k trips around the world may be so wildly counterintuitive that the statement might seemingly be in error, but please do not change the statement without first understanding the below math (shown here with excess precision):

Paper thickness = 0.0030 inch = 0.0000762 m (0.003 × 25.4 mm/inch ÷ 1000 mm/m)
Earth’s mean circumfrence = 40,041,470 m

In then follows that…

146,386.7 trips × 40,041,470 m × 0.013E-15 = 0.0000762 m = 0.0030 inch = paper thickness
-->

==Alternatives to parts-per notation==
====SI-compliant expressions====
In the [[English language]], [[Names of large numbers|named numbers]] have a consistent meaning only up to “[[million]].” Starting with “[[billion]],” there are ''two'' numbering conventions: the [[long and short scales|“long” and “short” scales]], and “billion” can mean either 10<sup>9</sup> or 10<sup>12</sup>.

For most of the [[19th century|19th]] and [[20th century|20th centuries]], the [[United Kingdom]] uniformly used the long scale, while the [[United States|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 language|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.<ref name="BIPM"/> 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.”''<span style="margin-left:0.3em"><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]''<sub>&nbsp;</sub></ref> Note however, that the NIST’s stated premiss for its position is only partially true; “million” has only ''one'' meaning in all languages. Note too, 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.<sub>&nbsp;</sub></ref></span>

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 <font color=maroon>maroon</font> text in the chart below.

{|border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0em; background: #f5f5f0; border: 3px #2F2F2F solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="5" style="background:#535353" align="center"|<font color=white>NOTATIONS FOR DIMENSIONLESS QUANTITIES</font>
|-
|style="background:#d9d9d3" align="center"|'''Measure'''
|style="background:#d9d9d3" align="center"|'''SI<br>units'''
|style="background:#d9d9d3" align="center"|'''Named<br>parts-per ratio'''
|style="background:#d9d9d3" align="center"|'''Parts-per<br>abbreviation<br>or symbol'''
|style="background:#d9d9d3" align="center"|'''Value in<br>scientific<br>notation'''
|-
|style="background:#d9d9d3" align="right"|A [[Strain (materials science)|strain]] of…
|align="center"|2 [[Centi-|c]]<nowiki></nowiki>m/m
|align="center"|2 parts per hundred
|align="center"|&nbsp;&nbsp;&nbsp; 2% <ref>Compliance with the SI regarding the percent symbol (%) is limited in this chart. According to the BIPM’s [http://www.bipm.org/en/si/si_brochure/chapter5/5-3-2.html#5-3-3 SI brochure: Subsection 5.3.3, ''Formatting the value of a quantity''], a space is always used to separate the unit symbol from the numeric value. Notable exceptions are the unit symbols for degree, minute, and second for plane angle, °, ′, and ″ (e.g., a latitude of 47°&nbsp;38′). However, according to [http://www.bipm.org/en/si/si_brochure/chapter5/5-3-7.html 5.3.7 ''Stating values of dimensionless quantities, or quantities of dimension one]'', the exception does not apply to the “%” symbol; it states as follows: ''“When it [the percent symbol] is used, a space separates the number and the symbol %.”'' This practice has not been well adopted with regard to the % symbol, is [[Wikipedia:Manual_of_Style#Percentages|contrary to Wikipedia’s ''Manual of Style'']], and is not observed here.<sub>&nbsp;</sub></ref>
|align="center"|2&nbsp;×&nbsp;10<sup>–2</sup>
|-
|style="background:#d9d9d3" align="right"|A sensitivity of…
|align="center"|2 [[Milli-|m]]V/V
|align="center"|2 parts per thousand
|align="center"|<font color=maroon>2 ‰</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–3</sup>
|-
|style="background:#d9d9d3" align="right"|A sensitivity of…
|align="center"|0.2 mV/V
|align="center"|2 parts per ten thousand
|align="center"|<font color=maroon>2 ‱</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–4</sup>
|-
|style="background:#d9d9d3" align="right"|A sensitivity of…
|align="center"|2 [[Micro-|µ]]V/V
|align="center"|2 parts per million
|align="center"|2 ppm
|align="center"|2&nbsp;×&nbsp;10<sup>–6</sup>
|-
|style="background:#d9d9d3" align="right"|A sensitivity of…
|align="center"|2 [[Nano-|n]]V/V
|align="center"|<font color=maroon>2 parts per billion</font>
|align="center"|<font color=maroon>2 ppb</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–9</sup>
|-
|style="background:#d9d9d3" align="right"|A sensitivity of…
|align="center"|2 [[Pico-|p]]V/V
|align="center"|<font color=maroon>2 parts per trillion</font>
|align="center"|<font color=maroon>2 ppt</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–12</sup>
|-
|style="background:#d9d9d3" align="right"|A mass concentration of…
|align="center"|2 mg/kg
|align="center"|2 parts per million
|align="center"|2 ppm
|align="center"|2&nbsp;×&nbsp;10<sup>–6</sup>
|-
|style="background:#d9d9d3" align="right"|A mass concentration of…
|align="center"|2 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 or micro (m or µ), 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.-->
|align="center"|<font color=maroon>2 parts per billion</font>
|align="center"|<font color=maroon>2 ppb</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–9</sup>
|-
|style="background:#d9d9d3" align="right"|A mass concentration of…
|align="center"|2 ng/kg
|align="center"|<font color=maroon>2 parts per trillion</font>
|align="center"|<font color=maroon>2 ppt</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–12</sup>
|-
|style="background:#d9d9d3" align="right"|A mass concentration of…
|align="center"|2 pg/kg
|align="center"|<font color=maroon>2 parts per quadrillion</font>
|align="center"|<font color=maroon>2 ppq</font>
|align="center"|2&nbsp;×&nbsp;10<sup>–15</sup>
|-
|style="background:#d9d9d3" align="right"|A stability of…
|align="center"|1 (µA/A)/min.
|align="center"|1 part per million per min.
|align="center"|1 ppm/min.
|align="center"|1&nbsp;×&nbsp;10<sup>–6</sup>/min.
|-
|style="background:#d9d9d3" align="right"|A change of…
|align="center"|5 nΩ/Ω
|align="center"|<font color=maroon>5 parts per billion</font>
|align="center"|<font color=maroon>5 ppb</font>
|align="center"|5&nbsp;×&nbsp;10<sup>–9</sup>
|-
|style="background:#d9d9d3" align="right"|An uncertainty of…
|align="center"|9 µg/kg
|align="center"|<font color=maroon>9 parts per billion</font>
|align="center"|<font color=maroon>9 ppb</font>
|align="center"|9&nbsp;×&nbsp;10<sup>–9</sup>
|-
|style="background:#d9d9d3" align="right"|A shift of…
|align="center"|1 nm/m
|align="center"|<font color=maroon>1 part per billion</font>
|align="center"|<font color=maroon>1 ppb</font>
|align="center"|1&nbsp;×&nbsp;10<sup>–9</sup>
|-
|style="background:#d9d9d3" align="right"|A strain of…
|align="center"|1 µm/m
|align="center"|1 part per million
|align="center"|1 ppm
|align="center"|1&nbsp;×&nbsp;10<sup>–6</sup>
|-
|style="background:#d9d9d3" align="right"|A [[temperature coefficient]] of…
|align="center"|0.3 (µHz/Hz)/°C
|align="center"|0.3 part per million per °C
|align="center"|0.3 ppm/°C
|align="center"|0.3&nbsp;×&nbsp;10<sup>–6</sup>/°C
|-
|style="background:#d9d9d3" align="right"|A frequency change of…
|align="center"|0.35&nbsp;×&nbsp;10<sup>–9</sup> &#x0192;
|align="center"|<font color=maroon>0.35 part per billion</font>
|align="center"|<font color=maroon>0.35 ppb</font>
|align="center"|0.35&nbsp;×&nbsp;10<sup>–9</sup>
|}

Note that the notations in the “SI units” column above are all [[Dimensionless quantity|dimensionless quantities]]; that is, the units of measurement cancel in expressions like “1&nbsp;nm/m” (1&nbsp;n<strike>m</strike>/<strike>m</strike>&nbsp;= 1&nbsp;nano&nbsp;= 1&nbsp;×&nbsp;10<sup>–9</sup>) so the [[quotient]]s are pure-number [[coefficient]]s with values less than 1.

====Uno====
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"/> This symbol is not to be confused with the always-italicized symbol for the variable ‘uncertainty’ (symbol: ''U).'' This unit name uno and its symbol could be used in combination with the [[SI prefix]]es to express the values of dimensionless quantities which are much less—or even ''greater—''than one.<ref>Certain mathematical functions can produce proportional quantities with values greater than 1.<sub>&nbsp;</sub></ref>

Common parts-per notations in terms of the uno are given in the table below.

{|border="1" cellpadding="4" cellspacing="0" style="margin: 1em 1em 1em 0em; background: #f5f5f0; border: 3px #2F2F2F solid; border-collapse: collapse; font-size: 95%;"
|-
! colspan="5" style="background:#535353" align="center"|<font color=white>IUPAP’S “UNO” PROPOSAL</font>
|-
|style="background:#d9d9d3" align="center"|'''Coefficient'''
|style="background:#d9d9d3" align="center"|'''Parts-<br>per<br>example'''
|style="background:#d9d9d3" align="center"|'''Uno<br><span style="margin-left:0.3em">equiv.'''</span>
|style="background:#d9d9d3" align="center"|'''Symbol<br>form'''
|style="background:#d9d9d3" align="center"|'''Value of<br><span style="margin-left:0.2em">quantity'''</span>
|-
|align="center"|10<sup>–2</sup>
|align="center"|2%
|align="center"|2 centiuno
|align="center"|2 cU
|align="left"|2&nbsp;×&nbsp;10<sup>–2</sup>
|-
|align="center"|10<sup>–3</sup>
|align="center"|2 ‰<!-- NOTE TO EDITORS: Unlike the % symbol, which constitutes a formatting exception to the rule of the SI, a space goes between the value and both the permille and permyriad symbols (‰ and ‱). Besides adhering to the rule of the SI, this is also good technical writing practice as it helps to distinguish these two, less-common symbols from the percent symbol so as to avoid confusion.--> 
|align="center"|2 milliuno
|align="center"|2 mU
|align="left"|2&nbsp;×&nbsp;10<sup>–3</sup>
|-
|align="center"|10<sup>–6</sup>
|align="center"|2 ppm
|align="center"|2 microuno
|align="center"|2 µU
|align="left"|2&nbsp;×&nbsp;10<sup>–6</sup>
|-
|align="center"|10<sup>–9</sup>
|align="center"|2 ppb
|align="center"|2 nanouno
|align="center"|2 nU
|align="left"|2&nbsp;×&nbsp;10<sup>–9</sup>
|-
|align="center"|10<sup>–12</sup>
|align="center"|2 ppt
|align="center"|2 picouno
|align="center"|2 pU
|align="left"|2&nbsp;×&nbsp;10<sup>–12</sup>
|}

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.”''<span style="margin-left:0.3em"><ref>''Report of the 16th meeting  (13–14 May 2004)'', by the Consultative Committee for Units, to the International Committee for Weights and Measures, of the International Bureau of Weights and Measures ([http://www.bipm.org/utils/common/pdf/CCU16.pdf 1.1&nbsp;MB PDF, here]).<sub>&nbsp;</sub></ref></span> 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.

==Improper applications of parts-per notation==
Parts-per notation may properly be used only to express true dimensionless quantities; that is, the units of measurement ''must'' cancel in expressions like “1&nbsp;mg/kg” so that the quotients are pure numbers with values less than 1. Mixed-unit quantities such as “a [[radon]] concentration of 15&nbsp;p[[Curie|Ci]]/[[Litre|L]]” are not dimensionless quantities and may not be expressed using any form of parts-per notation, such as “15&nbsp;ppt”.  Other examples of measures that are not dimensionless quantities are as follows:

* Particulate matter in the air: 50&nbsp;µg/m³  &nbsp;'''''but not''''':&nbsp; 50&nbsp;ppm
* A [[stepper motor]]/gear system that produces a motion of 1&nbsp;µm/pulse  &nbsp;'''''but not''''':&nbsp; 1&nbsp;ppm
* Mercury vapor concentration in air: 0.6&nbsp;ng/[[Litre|L]]  &nbsp;'''''but not''''':&nbsp; 0.6&nbsp;ppt<!--EDITORS NOTE: This example intentionally juxtaposes nano (one billionth) and ppt (parts per trillion) rather than ppb, as a lead-in to the below discussion regarding how what is commonly done with aqueous concentrations (where one liter of water has a mass of 1 kg) may not be done with air.-->

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&nbsp;ppm, 0.8&nbsp;ppb, etc.) and further, for those reports to state that the notations denote milligrams per [[Litre|liter]] or micrograms per liter. Whereas “2.1&nbsp;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<!-- EDITORS NOTE: The fact that water never gets denser than 0.999 974 95 kg/L (at 3.984 °C) is totally beyond the scope of this article. It must be understood that this super-high-precision value is for absolutely pure water of carefully controlled isotopic composition, (which contaminated water with suspended minerals is most certainly not). Further, analysis of water-borne pollutants are not performed at a precision of five or six digits; besides, concentrations of pollutants are nowhere near that stable over time. --> and that “2.1&nbsp;mg/kg” (2.1&nbsp;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.

==Convertibility to other units of measurement==
Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the [[coefficient of thermal expansion]] of a certain [[brass]] alloy, ''α''&nbsp;=&nbsp;18.7&nbsp;ppm/°C, may be expressed as 18.7&nbsp;([[Micrometre|µm]]/m)/°C, or as 18.7&nbsp;(µ[[Inch|in]]/in)/°C; the numeric value representing a relative proportion doesn’t change with the adoption of a different unit of measure.<ref>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 <sup>5</sup>⁄<sub>9</sub> that of a Celsius-sized interval, the value is typically expressed as 10.4&nbsp;(µin/in)/°F rather than 18.7&nbsp;(µin/in)/°C.<sub>&nbsp;</sub></ref> Similarly, a [[metering pump]] that injects a trace chemical into the main process line at the proportional flow rate ''[[Volumetric flow rate|Q]]<sub>p</sub>''&nbsp;=&nbsp;125&nbsp;ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125&nbsp;µL/L, 125&nbsp;µ[[Gallon|gal]]/gal, 125&nbsp;µ[[Cubic metre|(m³)]]/m³, etc.

== See also ==
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* [[International Bureau of Weights and Measures]] (BIPM)
* [[International Committee for Weights and Measures]] (CIPM)
* [[International Electrotechnical Commission]] (IEC)
* [[International Organization for Standardization]] (|SO)
* [[International System of Units]] (SI)
* [[Long and short scales]]
* [[Mole fraction]]
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* [[Names of large numbers]]
* [[National Institute of Standards and Technology]] (NIST)
* [[Percentage]] (%)
* [[Permille]] (‰)
* [[Basis point|Permyriad]] (‱) (Basis point)
* [[SI prefix|SI prefixes]]
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==References==
<references/>

==External links==
* National Institute of Standards and Technology (NIST): [http://www.nist.gov/ Home page]
* International Bureau of Weights and Measures (BIPM): [http://www.bipm.org/en/home/ Home page]


[[Category:Analytical chemistry]]
[[Category:Chemical nomenclature]]
[[Category:Dimensionless numbers]]
[[Category:Environmental chemistry]]
[[Category:Mathematical terminology]]
[[Category:Measurement]]
[[Category:Metrics]]
[[Category:Physical constants]]
[[Category:Units of measure]]

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