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## Parts-per notation ## Additional recommended knowledge
## OverviewParts-per notation is often used in the measure of dilutions (concentrations) in chemistry; for instance, to measure the relative abundance of dissolved minerals or pollutants in water. 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. Similarly, parts-per notation is used also in physics and engineering to express the value of various proportional phenomena. For instance, a special metal alloy might expand 1.2 micrometers per meter of length for every degree Celsius and this would be expressed as The above parts-per notations are all dimensionless quantities; that is, the units of measurement always cancel in expressions like “1 nanometer per meter” (1 n 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). ## Parts-per expressions*Parts 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}. This is equivalent to one drop of water in 5 milliliters (one spoon-full) or one second of time in 1⅔ minutes.*Parts per thousand*: Should be spelled out in full and should avoid the use the “ppt” abbreviation, which is generally 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 use the “ppt” abbreviation. “Parts 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 in 50 milliliters, or one second of time in 16⅔ minutes.*Parts per ten thousand*: Is a unit known as 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 ‱. Although rarely, if ever, used in science (ppm would instead be used), one permyriad has an unambiguous value of one part per 10,000 parts, one part in 10^{4}, and a value of 1 × 10^{–4}. This is equivalent to one drop of water in 500 milliliters, or one second of time in approximately 2¾ hours.*Parts per million*(**ppm**): Denotes one part per 1,000,000 parts, one part in 10^{6}, and a value of 1 × 10^{–6}. This is equivalent to one drop of water in 50 liters, or one second of time in approximately 11½ days.*Parts per billion*(**ppb**): Denotes one part per 1,000,000,000 parts, one part in 10^{9}, and a value of 1 × 10^{–9}. This is equivalent to 50 drops of water in an Olympic-size swimming pool, or one second of time in approximately 31.7 years.*Parts per trillion*(**ppt**): Denotes one part per 1,000,000,000,000 parts, one part in 10^{12}, and a value of 1 × 10^{–12}. This is equivalent to 1 drop of water in 20 Olympic-size swimming pools, or one second of time in approximately 31,700 years.*Parts per quadrillion*(**ppq**): Denotes one part per 1,000,000,000,000,000 parts, one part in 10^{15}, and a value of 1 × 10^{–15}. This is equivalent to 1 drop of water in a cube of water measuring approximately 368 meters on a side (a cube about as tall as the roof of the Empire State Building), or one second of time in approximately 31.7 million years.^{[3]}
## Alternatives to parts-per notation## SI-compliant expressionsIn the English language, named numbers have a consistent meaning only up to “million.” Starting with “billion,” there are For most of the 19th and 20th centuries, the United Kingdom uniformly used the long scale, while the United States of America used the short scale, so that the two systems were often referred to as “British” and “American” usage respectively. Today, the UK uses the short scale exclusively in official and mass media usage and, although some long-scale usage still continues, the terms “British” and “American” no longer reflect usage. See also 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. Because parts-per notations have generally well-understood meanings 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 maroon text in the chart below.
Note that the notations in the “SI units” column above are all dimensionless quantities; that is, the units of measurement cancel in expressions like “1 nm/m” (1 n ## The unoBecause 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. - 1 ppm = 1 microuno = 1 µU
- 1 ppb = 1 nanouno = 1 nU
- 1 ppt = 1 picouno = 1 pU
In 2004, a report to the International Committee for Weights and Measures (CIPM) stated that response to the proposal of the uno ## Improper applications of parts-per notationParts-per notation may properly be used only to express true dimensionless quantities; that is, the units of measurement - Particulate matter in the air: 50 µg/m³
: 50 ppm**but not** - A stepper motor/gear system that produces a motion of 1 µm/pulse
: 1 ppm**but not** - Mercury vapor concentration in air: 0.6 ng/L
: 0.6 ppt**but not**
Note however, that it is not uncommon to express aqueous concentrations—particularly in drinking-water reports intended for the general public—using parts-per notation (2.1 ppm, 0.8 ppb, etc.) and further, for those reports to state that the notations denote milligrams per liter or micrograms per liter. Whereas “2.1 mg/L” is technically not a dimensionless quantity on the face of it, it is well understood in scientific circles that one liter of water has a mass of one kilogram and that “2.1 mg/kg” (2.1 ppm) is the true measure. The goal in all technical writing (including drinking-water reports for the general public) is to clearly communicate to the intended audience with minimal confusion. Drinking water is intuitively a volumetric quantity in the public’s mind so measures of contamination expressed on a per-liter basis are considered to be easier to grasp. ## Convertibility to other units of measurementParts-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, ## See also
## References- ^
^{a}^{b}^{c}BIPM: 5.3.7*Stating values of dimensionless quantities, or quantities of dimension one* - ^
^{a}^{b}Report to the 1999 IUPAP General Assembly:*Report on recent Committee activities on behalf of IUPAP by Brian W Petley September 1998* **^**Measurements at parts in 10^{15}, though rather uncommon in analytic chemistry,*are*performed. Measurements of dioxin are routinely made at the*sub*-ppq level, as are various toxins that have hormone-like, biological effects. 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._{ }**^**NIST:*Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt*_{ }**^***Quantities and units*- Part 0:*General principles*, ISO 31-0:1992._{ }**^**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._{ }**^***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)._{ }**^**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. Since a Fahrenheit-sized interval of temperature is only^{5}⁄_{9}that of a Celsius-sized interval, the value is typically expressed as 10.4 (µin/in)/°F rather than 18.7 (µin/in)/°C._{ }
Categories: Analytical chemistry | Environmental chemistry |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Parts-per_notation". A list of authors is available in Wikipedia. |