Parts-per notation

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In science and engineering, parts-per notation is a set of pseudo units to describe small values ​​of dimensions without dimensions, e.g. mole fraction or mass fraction. Since these fragments are quantities of quantity per quantity, they are pure numbers without the corresponding measurement units. Commonly used is ppm (parts-per-million, 10 ^-6 ), ppb (part-by- billion, 10 ^-9 ), ppt (parts-per-trillion, 10 ^-12 ) and ppq (parts-per-quadrillion, 10 ^-15 ). This notation is not part of the SI system and its meaning is ambiguous.

Video Parts-per notation

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The per-piece notation is often used to describe a dilute solution in chemistry, for example, the relative abundance of dissolved minerals or water-borne pollutants. The "1 ppm" unit can be used for mass fractions if water-borne pollutants are present at one-million grams per gram of sample solution. When working with an aqueous solution, it is usually assumed that the water density is 1.00 g/mL. Therefore, it is common to equate 1 kilogram of water with 1 liter of water. As a result, 1 ppm corresponds to 1 mg/L and 1 ppb corresponds to 1? G/L.

Similarly, parts-per notation is also used in physics and techniques to express the value of various proportional phenomena. For example, special metal alloys can expand 1.2 micrometers per meter long for each degree Celsius and this would be expressed as "? Ã, = 1.2 ppm/Â ° C." The per-part notation is also used to indicate changes, stability, or uncertainty in measurement. For example, the accuracy of ground-survey distance measurements when using laser rangefinds may be 1 millimeter per kilometer distance; this can be expressed as "Accuracy = 1 ppm."

The part-per notation is all the dimensionless quantity: in mathematical expression, the unit of measurement is always canceled. In fractions such as "2 nanometers per meter" (2 m / m Ã, = 2Ã, nanoÃ, = 2 Ã,ÃÆ' â € "Ã, 10 ^-9 Ã, = 2Ã, ppbÃ, = 2Ã, ÃÆ' â € "0,000 000 001) so quotients are pure number coefficients with a positive value less than 1. When per-part notations, including the percent symbol (%), are used in ordinary prose (as opposed to mathematical expressions), they are still pure numbers without dimensions. However, they generally use the literal meaning of "parts per" ratio of the comparison (eg, "2 ppb" would generally be interpreted as "two parts in a billion parts").

The per-part notation can be expressed in any unit of the same size. For example, the coefficient of thermal expansion of a particular brass alloy, ? Ã, = Ã, 18,7Ã, ppm/Ã, Â ° C, can be expressed as 18.7 Ã, μ, , Âμin/in)/Ã, Â ° C; the numerical value representing the proportion is relatively unchanged with the adoption of different sized units. Similarly, metering pumps that inject chemicals into the main process path at a proportional flow rate of Ã, = Ã, 125Ã, ppm, do so at rates that may be expressed in various volumetric units, including 125 Ã,ÂμL/L, 125Ã,Âμgal/gal, 125Ã, cm ³ /m ³ , etc.

In nuclear magnetic resonance spectroscopy (NMR)

In nuclear magnetic resonance spectroscopy (NMR), chemical shifts are usually expressed in ppm. This represents the frequency difference measured in parts per million of the reference frequency. The reference frequency depends on the magnetic field of the instrument and the element being measured. Usually expressed in MHz. Typical chemical shifts rarely exceed several hundred Hz of reference frequencies, so chemical shifts are expressed easily in ppm (Hz/MHz). The per-part notation provides an unlimited quantity independent of the strength of the instrument field.

Maps Parts-per notation

Section-per expression

• One part per hundred is generally represented by a percent (%) symbol and represents one part per 100 parts, one part in 10 ² , and one value 1 Ã,ÃÆ' â € "10 ^-2 . This is equivalent to about fifteen minutes of a day.

• One part per thousand should generally be spelled full and not as "ppt" (which is usually understood to represent "parts per trillion"). It may also be denoted by the millage (?) Symbol. Note however, that special disciplines such as oceanography, as well as educational exercises, do not use the abbreviation "ppt". "One part per thousand" shows one part per 1000 parts, one part in 10 ³ , and a value of 1 Ã,ÃÆ' â € "10 ^-3 . This is equivalent to about one and a half minutes from one day.
• One part per ten thousand is denoted by a permyriad symbol (?). In contrast, in finance, the bottom line is quantity with dimensions (time ^-1 ) and is usually used to indicate a change or a difference between the percentage interest rate. For example, a change in the interest rate from 5.15% per year to 5.35% per annum can be represented as a 20 basis point change. Although rarely used in science (ppm is usually used instead), one permyriad has an unambiguous value of one part per part 000 , one part in 10 ⁴ , and a value of 1 Ã,ÃÆ' â € "10 ^-4 . This is equivalent to about nine seconds from one day.

• One part per million ppm ) shows one section per 1 000 < span> 000 section, one part in 10 ⁶ , 1 / 1 000 000 ÃÆ'â € "100% = 0,0001% (or 1% = 10 < span> 000 ppm), and a value of 1 Ã,ÃÆ' â € "10 ^-6 . This is equivalent to about 32 seconds a year; in distance measurement, it is equivalent to 1 mm error per km distance traveled.

• One part per billion ( ppb ) shows one section per 1 000 000 000 section, one part in 10 ⁹ , 1 / 1 000 000 000 ÃÆ'â € "100% = 0,000 0001 % (or 1% = 10 000 000 ppb) and value 1Ã, ÃÆ'â € "Ã, 10 ^-9 . This is equivalent to about three seconds from a century.

• One part per trillion ( ppt ) shows one section per 1 000 000 000 000 section, one part in 10 ¹² , and value 1Ã,ÃÆ' â € "10 ^-12 . This is equivalent to about three seconds out of every hundred thousand years.

• One section per quadrillion ( ppq ) shows one section per 1 000 000 000 000 000 section, one part in 10 ¹⁵ , and value 1Ã, ÃÆ' â € "Ã, 10 ^-15 . This equates to about two and a half minutes of the Earth's age (4.5 billion years). Although relatively rare in analytical chemistry, measurements at the ppq level are sometimes done.

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Criticism

Although the International Bureau of Weights and Measures (an international standard organization known also by its French initials BIPM) recognizes the use of part-by-notation, it is not formally part of the International System of Units (SI). Note that although "percent" (%) is not officially part of the SI, both BIPM and ISO take positions that "in mathematical expressions, internationally recognized symbols% (percent) can be used with SI to represent 0.01 " for a dimensionless number. According to IUPAP, "a source of continuing annoyance with puritan units is the continuous use of percent, ppm, ppb, and ppt." Although expressions corresponding to SI should be used as alternatives, their parts Notation -per remains widely used in technical disciplines. The main problems with per-part notation are as follows:

Long and short scale

Since numbers named starting with "billion" have different values ​​in different countries, BIPM recommends avoiding the use of "ppb" and "ppt" to prevent misunderstanding. The US National Institute of Standards and Technology (NIST) takes a strict position, stating that "a language-dependent term [.Ã,.Ã,.] Is unacceptable for use with SI to express quantity values."

Thousand vs. trillion

Although "ppt" usually means "parts per trillion", it sometimes means "parts per thousand". Unless the meaning of "ppt" is explicitly defined, it must be determined from the context.

Mass vs. vs. mole fraction vs. volume fraction

Another problem of per-part notation is that it can refer to mass fractions, mole fractions or volume fractions. Since it is not usually mentioned which quantity is used, it is better to write the unit as kg/kg, mole/mole or m ³ /m ³ (though they are all without dimensions). The difference is quite significant when dealing with gas and it is very important to determine the amount used. For example, the conversion factor between the mass fraction 1 ppb and the mole fraction of 1 ppb is about 4.7 for the CFC-11 greenhouse gas in the air. For volume fractions, the suffix "V" or "v" is sometimes added to the part-per notation (eg, ppmV, ppbv, pptv). Unfortunately, ppbv and pptv are also often used for mole fractions (which is identical to volume fractions only for ideal gases).

Usage is generally quite fixed within the most specific branch of science, leading some researchers to conclude that their own use (mass/mass, mole/mol, volume/volume, or the other) is the only true one. This, in turn, leads them to not specify their use in their publications, and others may therefore misinterpret their results. For example, electrochemical experts often use volume/volume, while chemical engineers may use mass/mass as well as volume/volume. Many excellent academic papers failed to determine the use of per-part notation.

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Expressions corresponding to SI

SI-compliant units that can be used as alternatives are shown in the chart below. The expressions BIPM explicitly do not recognize as being suitable for showing dimensionless dimensions with SI are shown in red text .

Note that the notation in the "SI Unit" column above is all dimensionless quantities; ie, the measurement factor units in expressions such as "1 nm/m" (1 s s $Ã,\; 10-9)\; so\; that\; quotients\; are\; the\; pure\; number\; coefficients\; with\; values\; ​​less\; than\; 1.$

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Uno

Due to the intricate nature of expressing a certain dimensionless number per SI guideline, the International Union of Applied and Applied Physics (IUPAP) in 1999 proposed the adoption of a special name "uno" (symbol: U) to represent number 1 in the dimensionless number. This symbol is not to be confused with a symbol that is always italicized for the "uncertainty" variable (symbol: U ). The name of the unit is "uno" and its symbol can be used in combination with the SI prefix to express much less dimensionless quantity values ​​- or even larger - than one.

The common part-not notation in uno is given in the table below.

In 2004, a report to the International Committee on Weights and Measures (also known by the French initials CIPM) stated that responses to the uno proposal "have been almost entirely negative" and principal supporters "recommend dropping the idea ". Until recently, uno has not been adopted by standard organizations and it seems unlikely that it would be the official way to express dimensionless (low-dimension) dimensionless values. The proposal is instructive, however, for the perceived shortcomings of the current option to show dimensional quantities.

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Incorrect app

The per-part notation can be used only to express the number without the actual dimension; ie, the measurement unit should cancel in an expression such as "1 mg/kg" so that quotients are pure numbers with values ​​less than 1. Mixed-number units such as "concentration radon 15 pCi/L" instead of a dimensionless dimension and can not be expressed using the form of part-per notation, such as "ppt". Other examples of sizes that are not dimensionless quantities are as follows:

• Particulate matter in air: 50 Âμg/m ³ ; not 50 ppb.
• A stepper motor/gear system that produces 1 Ã,Âμm/pulse motion; not 1 ppm
• Concentration of mercury vapor in the air: 0.6 ng/L; not 0.6 ppt

It should be noted, however, that it is not uncommon to express water concentrations - especially in drinking water reports aimed at the general public - using per-piece notation (2.1Ã, ppm, 0.8Ã, ppb, etc.) And furthermore, for reports the. to state that the notation shows milligrams per liter or micrograms per liter. Although "2.1 mg/L" is not a dimensionless quantity, it is assumed in a scientific circle that "2.1 mg/kg" (2.1 ppm) is the true measure because one liter of water has a mass of about one kilogram. The goal in all technical writing (including drinking water reports for the general public) is to communicate clearly to the intended audience with minimal confusion. Drinking water intuitively is a volumetric quantity in the public mind so that the size of contamination expressed on a per liter basis is considered more easily understood. However, technically possible, for example, to "dissolve" more than one liter of highly hydrophilic chemicals in 1 liter of water; per-part notation would be confusing when explaining its solubility in water (over one million parts per million), so one would simply declare the volume (or mass) that would dissolve into liter, instead.

When reporting air-borne density, a slightly different convention is used because the air is about 1000 times denser than water. In water, 1 Âμg/m ³ is roughly equivalent to parts-per-trillion while in the air, roughly equivalent to parts-per-billion. Note also, that in the case of air, this convention is less accurate. While a liter of water is almost exactly 1 kg, an air cubic meter is often taken as 1,143 kg - much less accurate, but still close enough for many practical uses.

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See also

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References

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External links

• National Institute of Standards and Technology (NIST): Home
• International Weighing and Measurement Bureau (BIPM): Home Page

Source of the article : Wikipedia