Editing Parts-per notation

{{Short description|Set of units to describe small values}}
{{Redirect|Parts per billion|the film|Parts per Billion{{!}}''Parts per Billion''}}
[[File:Fluorescein (2).jpg|thumb|upright|[[Fluorescein]] aqueous solutions, diluted from {{val|10000}} to 1{{nbsp}}part per million in intervals of ten-fold dilution.

At {{val|10000|u=ppm}} the solution is a deep red colour. As the concentration decreases the colour becomes orange, then a vibrant yellow, with the final 1{{nbsp}}ppm sample a very pale yellow.]]

In [[science]] and [[engineering]], the '''parts-per notation''' is a set of pseudo-units to describe the small values of miscellaneous [[dimensionless quantity|dimensionless quantities]], e.g. [[mole fraction]] or [[mass fraction (chemistry)|mass fraction]]. 

Since these [[fraction (mathematics)|fractions]] are quantity-per-quantity measures, they are pure numbers with no associated [[units of measurement]]. Commonly used are

* '''parts-per-million''' '''- ppm''', {{nowrap|10<sup>−6</sup>}}
* '''parts-per-billion''' '''- ppb''', {{nowrap|10<sup>−9</sup>}}
* '''parts-per-trillion''' '''- ppt''', {{nowrap|10<sup>−12</sup>}}
* '''parts-per-quadrillion''' '''- ppq''', {{nowrap|10<sup>−15</sup>}} 

This notation is not part of the [[International System of Units]] - SI system and its meaning is ambiguous.

== 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&nbsp;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 solution]]s, it is common to assume that the density of water is 1.00&nbsp;g/mL. Therefore, it is common to equate 1&nbsp;kilogram of water with 1&nbsp;L of water. Consequently, 1&nbsp;ppm corresponds to 1&nbsp;mg/L and 1&nbsp;ppb corresponds to 1&nbsp;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}}]] {{=}} 1.2 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."{{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: "Accuracy {{nobr|±(1 mm + 1 ppm)".}} Consequently, a distance measurement of only a few meters would still have an accuracy of ±1&nbsp;mm in this example.
}}

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 n <s>m</s> / <s>m</s> {{=}} 2 nano {{=}} 2×{{10^|−9}} {{=}} 2 ppb {{=}} 2 × {{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}}</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 some [[brass]] alloy, {{nobr|[[coefficient of thermal expansion|{{mvar|α}}]] {{=}} 18.7 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.{{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 {{sfrac| 5 |9}} that of a Celsius-sized interval, the value is typically expressed as {{nobr|10.4 (μ [[inch|in]]/[[inch|in]])/°F}} rather than {{nobr|18.7 (μ [[inch|in]]/[[inch|in]])/°C.}}
}}
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}} {{=}} 12 ppm,}} is doing so at a rate that may be expressed in a variety of volumetric units, including {{nobr|125 μ[[litre|L]]/[[litre|L]],}} {{nobr|125 μ [[Gallon|gal]] / [[Gallon|gal]],}} 125&nbsp;cm<sup>3</sup>/[[cubic metre|m<sup>3</sup>]], etc.

In [[nuclear magnetic resonance spectroscopy]] (NMR), [[chemical shift]] is usually expressed in ppm. It represents the difference of a measured frequency in parts per million from the reference frequency. The reference frequency depends on the instrument's magnetic field and the element being measured. It is usually expressed in [[MHz]]. Typical chemical shifts are rarely more than a few hundred Hz from the reference frequency, so chemical shifts are conveniently expressed in ppm ([[Hertz (unit)|Hz]]/MHz). Parts-per notation gives a dimensionless quantity that does not depend on the instrument's field strength.

==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 that one xxxx of water has a volume of 0.05 ml (20 xxxx per milliliter).-->
{| class="wikitable" style="font-size:85%;line-height:0.9;text-align:center;margin-left:1ex;float:right;"
!style="padding:0 1px;"|1 of →<br />= ⭨<br />of ↓ &nbsp;
!per<br />cent<br />(%)
!per<br />mille<br />(‰)
!per<br />10,000<br />(‱)
!per<br />100,000<br />(pcm)
!per<br />million<br />(ppm)
!per<br />billion<br />(ppb)
|-
!%
|1||0.1||0.01||0.001||0.0001||{{10^|-7}}
|-
!‰
|10||1||0.1||0.01||0.001||{{10^|-6}}
|-
!‱
|100||10||1||0.1||0.01||{{10^|-5}}
|-
!pcm
|1,000||100||10||1||0.1||0.0001
|-
!ppm
|10,000||1,000||100||10||1||0.001
|-
!ppb
|{{10^|7}}||{{10^|6}}||{{10^|5}}||10,000||1,000||1
|}
{{visualisation_parts_per.svg}}
*''One part per [[100|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 fourteen minutes out of one day.
{{anchor|Thousand}}
*''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 ninety seconds 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:

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 {{unicode|‱}}). 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.

--> 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<sup>−1</sup>).<ref>{{Cite web|url=https://corporatefinanceinstitute.com/resources/fixed-income/basis-points-bps-definition/|title=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.
{{anchor|ppm}}
* ''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&nbsp;mm of error per km of distance traversed. In [[mining]], it is also equivalent to one [[gram]] per [[metric ton]], expressed as g/t.
{{anchor|ppb}}
* ''One part per [[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]].
{{anchor|ppt}}
* ''One part per [[Orders of magnitude (numbers)#1012|trillion]]'' ('''ppt''') denotes one part per 1,000,000,000,000 ({{10^|12}}) parts, and a value of {{10^|-12}}. This is equivalent to about thirty seconds out of every million years.
{{anchor|ppq}}
* ''One part per [[Orders of magnitude (numbers)#1015|quadrillion]]'' ('''ppq''') denotes one part per 1,000,000,000,000,000 ({{10^|15}}) parts, and a value of {{10^|-15}}. This is equivalent to about two and a half minutes out of the [[age of the Earth]] (4.5 billion years). Although relatively uncommon in analytical chemistry, measurements at the ppq level are sometimes performed.<ref>
Measurements of [[Polychlorinated dibenzodioxins|dioxin]] are routinely made at the ''sub''-ppq level. The [[United States Environmental Protection Agency|U.S. Environmental Protection Agency]] (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; 0.013&nbsp;ppq is equivalent to the thickness of a sheet of paper versus a journey of {{val|146000}} trips around the world.<sub>&nbsp;</sub></ref> <!-- EDITORS NOTE REGARDING {{val|146000}} 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 ÷ 1,000 mm/m)
Earth's mean circumference = 40,041,470 m

In then follows that...
[[File:Image-Olympic Pool Munich 1972, color adj.jpg|thumb|One part per [[trillion (short scale)|trillion]] (1&nbsp;ppt) is a proportion equivalent to a drop of water diluted into 400 [[Olympic-size swimming pool]]s.]]

In [[science]] and [[engineering]], the '''parts-per notation''' is a set of pseudo-units to describe

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

== Criticism ==
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.

=== Long and short scales ===
{{main|Long and short scales}}
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>

=== Thousand vs. trillion ===
Although "ppt" usually means "parts per trillion", it occasionally means "parts per thousand". Unless the meaning of "ppt" is defined explicitly, it has to be determined from the context.{{citation needed|date=May 2020}}

=== Mass fraction vs. mole fraction vs. volume fraction ===
Another problem of the parts-per notation is that it may refer to [[Mass fraction (chemistry)|mass fraction]], [[mole fraction]] or [[volume fraction]]. Since it is usually not stated which quantity is used, it is better to write the units out, such as kg/kg, mol/mol or m<sup>3</sup>/m<sup>3</sup>, even though they are all dimensionless.<ref>{{cite journal |last1=Schwartz |first1=S.E. |last2=Warneck |first2=P. |title=Units for use in atmospheric chemistry (IUPAC Recommendations 1995) |journal=Pure and Applied Chemistry |date=1995 |volume=67 |issue=8–9 |pages=1377–1406 |doi=10.1351/pac199567081377|url=http://www.iupac.org/publications/pac/1995/pdf/6708x1377.pdf| s2cid = 7029702}}</ref> The difference is quite significant when dealing with gases, and it is very important to specify which quantity is being used. For example, the conversion factor between a mass fraction of 1&nbsp;ppb and a mole fraction of 1&nbsp;ppb is about 4.7 for the greenhouse gas [[CFC-11]] in air (Molar mass of CFC-11 / Mean molar mass of air = 137.368 / 28.97 = 4.74). For volume fraction, the suffix "V" or "v" is sometimes appended to the parts-per notation (e.g. ppmV, ppbv, pptv).<ref>{{cite web |title=EPA on-line tools for site assessment calculation: Indoor air unit Conversion |publisher=[[United States Environmental Protection Agency|Environmental Protection Agency]] |url=http://www.epa.gov/athens/learn2model/part-two/onsite/ia_unit_conversion.html}}</ref><ref>{{cite book |author=Beychok, Milton R. |year=2005 |article=Air dispersion modeling conversions and formulas |title=Fundamentals of Stack Gas Dispersion |edition=4th |publisher=Milton R. Beychok |isbn=0964458802 |url=https://archive.org/details/fundamentalsofst0000beyc |url-access=registration}}</ref> However, ppbv and pptv are usually used to mean mole fractions{{dash}}"volume fraction" would literally mean what volume of a pure substance is included in a given volume of a mixture, and this is rarely used except in the case of [[alcohol by volume]].

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 green engineering |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 within each specific branch of science, but often in a way that is inconsistent with its usage in other branches, leading some researchers to assume that their own usage (mass/mass, mol/mol, volume/volume, mass/volume, or others) is correct and that other usages are incorrect. This assumption 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, many academic publications of otherwise excellent level fail to specify their use 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}}

== SI-compliant expressions ==
SI-compliant units that can be used as alternatives are shown in the chart below. Expressions that the BIPM explicitly does not recognize as being suitable for denoting dimensionless quantities with the SI are marked with <span style="color:darkred;">'''!'''</span>.

{|class="wikitable" style="font-size: 95%;"
|+ Notations for dimensionless quantities
|-
! Measure
! SI<br>units
! Named<br>parts-per ratio<br>(short scale)
! Parts-per<br>abbreviation<br>or symbol
! Value in<br>scientific<br>notation
|-
|style="background:#f2f2f2" align="right"| A [[Strain (materials science)|strain]] of...
|align="center"|2 [[Centimetre|cm]]/[[metre|m]]
|align="center"|2 parts per hundred
|align="center"|&nbsp;&nbsp;&nbsp; 2%<ref>According to [http://www.bipm.org/en/publications/si-brochure/section5-3-7.html BIPM's SI brochure, section 5.3.7], "When [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 [[WP:%|contrary to Wikipedia's ''Manual of Style'']], and is not observed here.</ref>
|align="center"|2&nbsp;×&nbsp;10<sup>−2</sup>
|-
|style="background:#f2f2f2" align="right"| A sensitivity of...
|align="center"|2 [[Milli-|m]]V/V
|align="center"|2 parts per thousand
|align="center"|2 ‰ <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−3</sup>
|-
|style="background:#f2f2f2" align="right"| A sensitivity of...
|align="center"|0.2 mV/V
|align="center"|2 parts per ten thousand
|align="center"|2 ‱ <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−4</sup>
|-
|style="background:#f2f2f2" 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:#f2f2f2" align="right"| A sensitivity of...
|align="center"|2 [[Nano-|n]]V/V
|align="center"|2 parts per billion <span style="color:darkred;">'''!'''</span>
|align="center"|2 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| A sensitivity of...
|align="center"|2 [[Pico-|p]]V/V
|align="center"|2 parts per trillion <span style="color:darkred;">'''!'''</span>
|align="center"|2 ppt <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−12</sup>
|-
|style="background:#f2f2f2" align="right"| A mass fraction of...
|align="center"|2&nbsp;mg/kg
|align="center"|2 parts per million
|align="center"|2 ppm
|align="center"|2&nbsp;×&nbsp;10<sup>−6</sup>
|-
|style="background:#f2f2f2" align="right"| A mass fraction of...
|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 (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"|2 parts per billion <span style="color:darkred;">'''!'''</span>
|align="center"|2 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| A mass fraction of...
|align="center"|2&nbsp;ng/kg
|align="center"|2 parts per trillion <span style="color:darkred;">'''!'''</span>
|align="center"|2 ppt <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−12</sup>
|-
|style="background:#f2f2f2" align="right"| A mass fraction of...
|align="center"|2 pg/kg
|align="center"|2 parts per quadrillion <span style="color:darkred;">'''!'''</span>
|align="center"|2 ppq <span style="color:darkred;">'''!'''</span>
|align="center"|2&nbsp;×&nbsp;10<sup>−15</sup>
|-
|style="background:#f2f2f2" align="right"| A volume fraction of...
|align="center"|5.2 μL/L
|align="center"|5.2 parts per million
|align="center"|5.2 ppm
|align="center"|5.2&nbsp;×&nbsp;10<sup>−6</sup>
|-
|style="background:#f2f2f2" align="right"| A mole fraction of...
|align="center"|5.24 μmol/mol
|align="center"|5.24 parts per million
|align="center"|5.24 ppm
|align="center"|5.24&nbsp;×&nbsp;10<sup>−6</sup>
|-
|style="background:#f2f2f2" align="right"| A mole fraction of...
|align="center"|5.24 nmol/mol
|align="center"|5.24 parts per billion <span style="color:darkred;">'''!'''</span>
|align="center"|5.24 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|5.24&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| A mole fraction of...
|align="center"|5.24 pmol/mol
|align="center"|5.24 parts per trillion <span style="color:darkred;">'''!'''</span>
|align="center"|5.24 ppt <span style="color:darkred;">'''!'''</span>
|align="center"|5.24&nbsp;×&nbsp;10<sup>−12</sup>
|-
|style="background:#f2f2f2" align="right"| A stability of...
|align="center"|1 (μA/A)/[[minute|min]]
|align="center"|1 part per million per minute
|align="center"|1 ppm/min
|align="center"|1&nbsp;×&nbsp;10<sup>−6</sup>/min
|-
|style="background:#f2f2f2" align="right"| A change of...
|align="center"|5 nΩ/Ω
|align="center"|5 parts per billion <span style="color:darkred;">'''!'''</span>
|align="center"|5 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|5&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| An uncertainty of...
|align="center"|9&nbsp;μg/kg
|align="center"|9 parts per billion <span style="color:darkred;">'''!'''</span>
|align="center"|9 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|9&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| A shift of...
|align="center"|1&nbsp;nm/m
|align="center"|1 part per billion <span style="color:darkred;">'''!'''</span>
|align="center"|1 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|1&nbsp;×&nbsp;10<sup>−9</sup>
|-
|style="background:#f2f2f2" align="right"| A strain of...
|align="center"|1&nbsp;μm/m
|align="center"|1 part per million
|align="center"|1 ppm
|align="center"|1&nbsp;×&nbsp;10<sup>−6</sup>
|-
|style="background:#f2f2f2" 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:#f2f2f2" align="right"| A frequency change of...
|align="center"|0.35&nbsp;×&nbsp;10<sup>−9</sup> ƒ
|align="center"|0.35 part per billion <span style="color:darkred;">'''!'''</span>
|align="center"|0.35 ppb <span style="color:darkred;">'''!'''</span>
|align="center"|0.35&nbsp;×&nbsp;10<sup>−9</sup>
|}

Note that the notations in the "SI units" column above are for 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;×&nbsp;10<sup>−9</sup>) so the [[ratio]]s are pure-number [[coefficient]]s with values less than 1.

==Uno (proposed dimensionless unit){{anchor|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" /> 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]].

==Footnotes==
{{notelist}}

==See also==
* [[International Electrotechnical Commission]] (IEC)
* [[Milligram per cent]]
* [[Percentage]] (%) 1 part in 100
* [[permille|Per mille]] (‰) 1 part in 1,000
* [[Permyriad]] (‱) 1 part in 10,000
* [[Per cent mille]] (pcm) 1 part in 100,000
* [[Per-unit system]]

==References==
{{Reflist}}

==External links==
{{wiktionary|ppm|ppb|ppt|ppq}}
* {{Commonscatinline}}
* [https://www.nist.gov/ National Institute of Standards and Technology] (NIST)
* [https://www.bipm.org/en/ International Bureau of Weights and Measures] (BIPM)

[[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 measurement]]