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 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. Science (from the Latin scientia, meaning " Knowledge " or "knowing" is the effort to discover, and increase human understanding Engineering is the Discipline and Profession of applying technical and scientific Knowledge and This article is about proportionality the mathematical relation Since parts-per notations are quantity-per-quantity measures, they are known as dimensionless quantities; that is, they are pure numbers with no associated units of measurement. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units 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 coefficients with values less than 1. In Mathematics, a coefficient is a Constant multiplicative factor of a certain object

## Overview

Parts-per notation is often used in the measure of dilutions (concentrations) in chemistry; for instance, for measuring the relative abundance of dissolved minerals or pollutants in water. In Chemistry, concentration is the measure of how much of a given substance there is mixed with another substance Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties The expression “1 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. For other uses of the words gram or gramme see Gram (disambiguation.

Similarly, parts-per notation is used also in physics and engineering to express the value of various proportional phenomena. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Engineering is the Discipline and Profession of applying technical and scientific Knowledge and 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. A micrometre ( American spelling: micrometer; symbol µm) is one millionth of a Metre, or equivalently one thousandth of a Millimetre The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The Celsius Temperature scale was previously known as the centigrade scale. When the Temperature of a substance changes the energy that is stored in the Intermolecular bonds between atoms changes 2 ppm/°C. ” Parts-per notation is also employed to denote the change, stability, or uncertainty in measurements. In Probability and Statistics, the standard deviation is a measure of the dispersion of a collection of values For instance, the accuracy of land-survey distance measurements when using a laser rangefinder might be 1 mm per km of distance; this could be expressed as “Accuracy = 1 ppm. The Millimetre ( American spelling: millimeter, symbol mm) is a unit of Length in the Metric system, equal to The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand[1]

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 nm/m = 2 nano = 2 × 10–9 = 2 ppb = 2 × 0. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units 000000001) so the quotients are pure-number coefficients with values less than 1. In Mathematics, a quotient is the result of a division. For example when dividing 6 by 3 the quotient is 2 while 6 is called the dividend, and 3 the In Mathematics, a coefficient is a Constant multiplicative factor of a certain object 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. In Mathematics, a percentage is a way of expressing a number as a Fraction of 100 ( per cent meaning "per hundred" g. , “2 ppb” would generally be interpreted as “two parts in a billion parts”). [2]

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). The International Bureau of Weights and Measures ( Bureau international des poids et mesures, in French) is an international Standards organization, one This article is about the country For a topic outline on this subject see List of basic France topics. [2] Consequently, according to IUPAP, “a continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt. The International Union of Pure and Applied Physics ( IUPAP) is an international Non-governmental organization devoted to the advancement of Physics.[3] 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. Names of numbers larger than a quadrillion are almost never used for reasons discussed further below The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French 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.

## Parts-per expressions

• One part per hundred: Should be represented by the percent (%) symbol and denotes one part per 100 parts, one part in 102, and a value of 1 × 10–2. In Mathematics, a percentage is a way of expressing a number as a Fraction of 100 ( per cent meaning "per hundred" This is equivalent to one drop of water diluted into 5 milliliters (one spoon-full) or one second of time in 1⅔ minutes. The litre or liter (see spelling differences) is a unit of Volume. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units A minute is a Unit of measurement of Time or of Angle. The minute is a unit of Time equal to 1/60th of an Hour or 60
• One part per thousand: Should be spelled out in full and should avoid the use the “ppt” abbreviation, which is usually understood to represent “parts per trillion”. It may also be denoted by the permille (‰) symbol. A per mil or per mille (also spelled permil, per mill or promille) ( Latin, literally meaning 'for (every thousand' is a tenth 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 103, and a value of 1 × 10–3. 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 ten thousand: Is denoted by the permyriad (‱) symbol. This list compares various sizes of positive Numbers including counts of things Dimensionless quantity and probabilities. 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. The field of finance refers to the concepts of Time, Money and Risk and how they are interrelated A basis point (often denoted as bp or ‱ rarely permyriad) is a unit that is equal to 1/100th of a Percentage point. 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 ‱. 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 104, and a value of 1 × 10–4. This is equivalent to one drop of water diluted into half a liter, or one second of time in approximately 2¾ hours. The litre or liter (see spelling differences) is a unit of Volume.
• One part per million (ppm): Denotes one part per 1,000,000 parts, one part in 106, and a value of 1 × 10–6. The word million In standard English, the -lli- in million is pronounced with an l-sound followed by a 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 billion (ppb): Denotes one part per 1,000,000,000 parts, one part in 109, and a value of 1 × 10–9. This is equivalent to 1 drop of water diluted into 250 chemical drums (50 m³), or one second of time in approximately 31. 7 years.
• One part per trillion (ppt): Denotes one part per 1,000,000,000,000 parts, one part in 1012, and a value of 1 × 10–12. This list compares various sizes of positive Numbers including counts of things Dimensionless quantity and probabilities. This is equivalent to 1 drop of water diluted into 20, two-meter-deep Olympic-size swimming pools (50,000 m³), or one second of time in approximately 31,700 years. An Olympic-size swimming pool is the type of Swimming pool used in the Olympic Games and other "long course" events
• One part per quadrillion (ppq): Denotes one part per 1,000,000,000,000,000 parts, one part in 1015, and a value of 1 × 10–15. This list compares various sizes of positive Numbers including counts of things Dimensionless quantity and probabilities. 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. The Empire State Building is a 102-story Art Deco Skyscraper in New York City at the intersection of Fifth Avenue and West 34th Street 7 million years. Although relatively uncommon in analytic chemistry, measurements at the ppq level are performed. [4]

## Alternatives to parts-per notation

#### SI-compliant expressions

In the English language, named numbers have a consistent meaning only up to “million”. English is a West Germanic language originating in England and is the First language for most people in the United Kingdom, the United States Names of numbers larger than a quadrillion are almost never used for reasons discussed further below The word million In standard English, the -lli- in million is pronounced with an l-sound followed by a Starting with “billion”, there are two numbering conventions: the “long” and “short” scales, and “billion” can mean either 109 or 1012. The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French

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. The 19th century of the Common Era began on January 1, 1801 and ended on December 31, 1900, according to the Gregorian calendar The twentieth century of the Common Era began on The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom, the UK or Britain,is a Sovereign state located The United States of America —commonly referred to as the 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. "Popular press" redirects here note that the University of Wisconsin Press publishes under the imprint "The Popular Press" See also Long and short scales. The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French However, the long scale is dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. Continental Europe, also referred to as mainland Europe or simply the Continent, is the Continent of Europe, explicitly excluding European See also Names of large numbers. Names of numbers larger than a quadrillion are almost never used for reasons discussed further below

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. [2] 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. ”[5] 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. In Mathematics, a percentage is a way of expressing a number as a Fraction of 100 ( per cent meaning "per hundred" 01” for dimensionless quantities. [2][6]

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
MeasureSI
units
Named
parts-per ratio
Parts-per
abbreviation
or symbol
Value in
scientific
notation
A strain of…2 cm/m2 parts per hundred    2% [7]2 × 10–2
A sensitivity of…2 mV/V2 parts per thousand2 ‰2 × 10–3
A sensitivity of…0. centi- (symbol c) is a SI prefix in the SI system of units denoting a factor of 10−2 or 1/100 "Milli" redirects here for the village in Azerbaijan see Birinci Milli; for similar-sounding words see Millie. 2 mV/V2 parts per ten thousand2 ‱2 × 10–4
A sensitivity of…2 µV/V2 parts per million2 ppm2 × 10–6
A sensitivity of…2 nV/V2 parts per billion2 ppb2 × 10–9
A sensitivity of…2 pV/V2 parts per trillion2 ppt2 × 10–12
A mass concentration of…2 mg/kg2 parts per million2 ppm2 × 10–6
A mass concentration of…2 µg/kg2 parts per billion2 ppb2 × 10–9
A mass concentration of…2 ng/kg2 parts per trillion2 ppt2 × 10–12
A mass concentration of…2 pg/kg2 parts per quadrillion2 ppq2 × 10–15
A stability of…1 (µA/A)/min. micro- ( µ) is a prefix in the SI and other systems of units denoting a factor of 10&minus6 (one Millionth. nano- is a prefix (symbol n) in the SI system of units denoting a factor of 10−9 pico- (symbol p) is a prefix denoting a factor of 10-12 in the International System of Units (SI 1 part per million per min. 1 ppm/min. 1 × 10–6/min.
A change of…5 nΩ/Ω5 parts per billion5 ppb5 × 10–9
An uncertainty of…9 µg/kg9 parts per billion9 ppb9 × 10–9
A shift of…1 nm/m1 part per billion1 ppb1 × 10–9
A strain of…1 µm/m1 part per million1 ppm1 × 10–6
A temperature coefficient of…0. The temperature coefficient is the relative change of a physical property when the Temperature is changed by 1  K. 3 (µHz/Hz)/°C0. 3 part per million per °C0. 3 ppm/°C0. 3 × 10–6/°C
A frequency change of…0. 35 × 10–9 ƒ0. 35 part per billion0. 35 ppb0. 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 nm/m = 1 nano = 1 × 10–9) so the quotients are pure-number coefficients with values less than 1. In Dimensional analysis, a dimensionless quantity (or more precisely a quantity with the dimensions of 1) is a Quantity without any Physical units In Mathematics, a quotient is the result of a division. For example when dividing 6 by 3 the quotient is 2 while 6 is called the dividend, and 3 the In Mathematics, a coefficient is a Constant multiplicative factor of a certain object

#### 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. The International Union of Pure and Applied Physics ( IUPAP) is an international Non-governmental organization devoted to the advancement of Physics. [3] 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 prefixes to express the values of dimensionless quantities which are much less—or even greater—than one. An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol to form a Decimal multiple or [8]

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

IUPAP’S “UNO” PROPOSAL
CoefficientParts-
per
example
Uno
equiv.
Symbol
form
Value of
quantity
10–22%2 centiuno2 cU2 × 10–2
10–32 ‰2 milliuno2 mU2 × 10–3
10–62 ppm2 microuno2 µU2 × 10–6
10–92 ppb2 nanouno2 nU2 × 10–9
10–122 ppt2 picouno2 pU2 × 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. The International Committee for Weights and Measures is the English name of the Comité international des poids et mesures ( CIPM, sometimes written in English [9] 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. A standards organization, standards body, standards development organization or SDO is any entity whose primary activities are developing coordinating 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 mg/kg” so that the quotients are pure numbers with values less than 1. Mixed-unit quantities such as “a radon concentration of 15 pCi/L” are not dimensionless quantities and may not be expressed using any form of parts-per notation, such as “15 ppt”. Radon (ˈreɪdɒn is the Chemical element that has the symbol Rn and Atomic number 86 A CURIE (short for Compact URI) is an abbreviated URI expressed in CURIE syntax and may be found in both XML and non-XML grammars The litre or liter (see spelling differences) is a unit of Volume. Other examples of measures that are not dimensionless quantities are as follows:

• Particulate matter in the air: 50 µg/m³  but not:  50 ppm
• A stepper motor/gear system that produces a motion of 1 µm/pulse  but not:  1 ppm
• Mercury vapor concentration in air: 0. A stepper motor (or step motor) is a brushless, synchronous Electric 6 ng/L  but not:  0. The litre or liter (see spelling differences) is a unit of Volume. 6 ppt

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. The litre or liter (see spelling differences) is a unit of Volume. 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. Technical writing, a form of Technical communication, is a style of formal writing used in fields as diverse as Computer Hardware and Software 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 = 18. When the Temperature of a substance changes the energy that is stored in the Intermolecular bonds between atoms changes Brass is any Alloy of Copper and Zinc; the proportions of zinc and copper can be varied to create a range of brasses with varying properties 7 ppm/°C, may be expressed as 18. 7 (µm/m)/°C, or as 18. A micrometre ( American spelling: micrometer; symbol µm) is one millionth of a Metre, or equivalently one thousandth of a Millimetre 7 (µin/in)/°C; the numeric value representing a relative proportion doesn’t change with the adoption of a different unit of measure. Inches redirects here To see the Les Savy Fav album see Inches. [10] Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Qp = 125 ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125 µL/L, 125 µgal/gal, 125 µ(m³)/m³, etc. A Metering pump is a Pump used to pump Liquids at adjustable Flow rates which are precise when averaged over time The volumetric flow rate in Fluid dynamics and Hydrometry, (also known as volume flow rate or rate of fluid flow) is the volume of fluid which A gallon is a measure of Volume. It is in current use in the United States and still has limited use in many other English-speaking countries CM3 redirects here If you were looking for the 3rd game in the Cooking Mama series abbreviated as CM3 see here.

 Names of large numbersNational Institute of Standards and Technology (NIST)Percentage (%)Permille (‰)Permyriad (‱) (Basis point)SI prefixes

## References

1. ^ This is a simplified explanation. The International Bureau of Weights and Measures ( Bureau international des poids et mesures, in French) is an international Standards organization, one The International Committee for Weights and Measures is the English name of the Comité international des poids et mesures ( CIPM, sometimes written in English The International Electrotechnical Commission ( IEC) is a not-for-profit, non-governmental international Standards organization that prepares and publishes The long and short scales are two different numerical systems used throughout the world Short scale is the English translation of the French In Chemistry, the mole fraction of a component in a Mixture is the relative proportion of molecules belonging to the component to those in the mixture Names of numbers larger than a quadrillion are almost never used for reasons discussed further below In Mathematics, a percentage is a way of expressing a number as a Fraction of 100 ( per cent meaning "per hundred" A per mil or per mille (also spelled permil, per mill or promille) ( Latin, literally meaning 'for (every thousand' is a tenth A basis point (often denoted as bp or ‱ rarely permyriad) is a unit that is equal to 1/100th of a Percentage point. An SI prefix (also known as a metric prefix) is a name or associated symbol that precedes a unit of measure (or its symbol to form a Decimal multiple or 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: ±(1 mm + 1 ppm). See also Grain and Film grain Granularity is a measure of the size of the components or descriptions of components that make up Consequently, a distance measurement of only a few meters would still have an accuracy of ±1 mm in this example.
2. ^ a b c d BIPM: 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one
3. ^ a b Report to the 1999 IUPAP General Assembly: Report on recent Committee activities on behalf of IUPAP by Brian W Petley September 1998
4. ^ The measurement of environmental toxins that have hormone-like, biological effects (e. g. , phthalates) are commonly performed at the ppq level. Phthalates, or phthalate esters, are esters of Phthalic acid and are mainly used as Plasticizers (substances added to Plastics to increase their Measurements of dioxin are routinely made at the sub-ppq level. Not to be confused with Dioxane or Digoxin. Dioxin is a heterocyclic, organic, antiaromatic compound The U.S. EPA currently sets a hard limit of 30 ppq for dioxin in drinking water but once recommended a voluntary limit of 0. 013 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 ppq is equivalent to the thickness of a sheet of paper versus a journey of 146,000 trips around the world.
5. ^ NIST: Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt
6. ^ Quantities and units - Part 0: General principles, ISO 31-0:1992.
7. ^ Compliance with the SI regarding the percent symbol (%) is limited in this chart. According to the BIPM’s 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° 38′). However, according to 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 contrary to Wikipedia’s Manual of Style, and is not observed here.
8. ^ Certain mathematical functions can produce proportional quantities with values greater than 1.
9. ^ 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 (1.1 MB PDF, here).
10. ^ In the particular case of coefficient of thermal expansion, the change to inches (one of the U.S. customary units) is typically also accompanied by a change to degrees Fahrenheit. US customary units, also known in the United States as English units or Imperial units (in reference to the British Empire) (but see English Fahrenheit is a temperature scale named after Daniel Gabriel Fahrenheit (1686–1736 a German Physicist who proposed it in 1724 Since a Fahrenheit-sized interval of temperature is only 59 that of a Celsius-sized interval, the value is typically expressed as 10. 4 (µin/in)/°F rather than 18. 7 (µin/in)/°C.