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Fluorescein aqueous solutions, diluted from 10000 to 1 part per million in intervals of ten-fold dilution. At 10000 ppm the solution is a deep red colour. As the concentration decreases the colour becomes orange, then a vibrant yellow, with the final 1 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 quantities, e.g. mole fraction or mass fraction.

Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are

  • parts-per-million – ppm, 10−6
  • parts-per-billion – ppb, 10−9
  • parts-per-trillion – ppt, 10−12
  • parts-per-quadrillion – ppq, 10−15

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

Applications

[edit]

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 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 solutions, it is common to assume that the density of water is 1.00 g/mL. Therefore, it is common to equate 1 kilogram of water with 1 L of water. Consequently, 1 ppm corresponds to 1 mg/L and 1 ppb corresponds to 1 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 micrometers per meter of length for every degree Celsius and this would be expressed as "α = 1.2 ppm/°C". Parts-per notation is also employed to denote the change, stability, or uncertainty in measurements. For instance, the accuracy of land-survey distance measurements when using a laser rangefinder might be 1 millimeter per kilometer of distance; this could be expressed as "Accuracy = 1 ppm."[a]

Parts-per notations are all dimensionless quantities: 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 × 0.000000001), so the quotients are pure-number coefficients with positive values less than or equal to 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 ppb" would generally be interpreted as "two parts in a billion parts").[1]

Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the expansion coefficient of some brass alloy, α = 18.7 ppm/°C, may be expressed as 18.7 (μm/m)/°C, or as 18.7 (μ in/in)/°C; the numeric value representing a relative proportion does not change with the adoption of a different unit of length.[b] Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Qp = 12 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 cm3/m3, 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 (Hz/MHz). Parts-per notation gives a dimensionless quantity that does not depend on the instrument's field strength.

Parts-per expressions

[edit]
1 of →
= ⭨
of ↓   		per
cent
(%) 		per
mille
(‰) 		per
myriad
(‱) 		per
cent mille
(pcm) 		per
million
(ppm) 		per
billion
(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 107 106 105 10,000 1,000 1
Visualisation of 1%, 1‰, 1‱, 1 pcm and 1 ppm as fractions of the large block (larger version)

  • One part per thousand should generally be spelled out in full and not as "ppt" (which is usually understood to represent "parts per trillion"). It may also be denoted by the 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 (103) 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 (104) parts, and a value of 10−4. This is equivalent to about nine seconds out of one day.
    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). 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−1).[2]
  • One part per hundred thousand, per cent mille (pcm) or milli-percent denotes one part per 100,000 (105) 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 cm of error per km of distance traversed.

  • One part per million (ppm) denotes one part per 1,000,000 (106) parts, and a value of 10−6. It is equivalent to about 32 seconds out of a year or 1 mm of error per km of distance traversed. In mining, it is also equivalent to one gram per metric ton, expressed as g/t.

  • One part per billion (ppb) denotes one part per 1,000,000,000 (109) parts, and a value of 10−9. This is equivalent to about three seconds out of a century.

  • One part per trillion (ppt) denotes one part per 1,000,000,000,000 (1012) parts, and a value of 10−12. This is equivalent to about thirty seconds out of every million years.

  • One part per quadrillion (ppq) denotes one part per 1,000,000,000,000,000 (1015) 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.[3]

Criticism

[edit]

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).[1] Note that although "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.[1][4] According to IUPAP, "a continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt".[5] Although 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

[edit]
Main article: Long and short scales

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. 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".[6]

Thousand vs. trillion

[edit]

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]

Mass fraction vs. mole fraction vs. volume fraction

[edit]

Another problem of the parts-per notation is that it may refer to 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 m3/m3, even though they are all dimensionless.[7] 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 ppb and a mole fraction of 1 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).[8][9] However, ppbv and pptv are usually used to mean mole fractions – "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).[10]

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, electrochemists often use volume/volume, while chemical engineers may use mass/mass as well as volume/volume, while chemists, the field of occupational safety and the field of permissible exposure limit (e.g. permitted gas exposure limit in air) may use mass/volume. Unfortunately, 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]

SI-compliant expressions

[edit]

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 !.

Notations for dimensionless quantities
Measure SI
units 		Named
parts-per ratio
(short scale) 		Parts-per
abbreviation
or symbol 		Value in
scientific
notation
A strain of... 2 cm/m 2 parts per hundred     2%[11] 2 × 10−2
A sensitivity of... 2 mV/V 2 parts per thousand 2 ‰ ! 2 × 10−3
A sensitivity of... 0.2 mV/V 2 parts per ten thousand 2 ‱ ! 2 × 10−4
A sensitivity of... 2 μV/V 2 parts per million 2 ppm 2 × 10−6
A sensitivity of... 2 nV/V 2 parts per billion ! 2 ppb ! 2 × 10−9
A sensitivity of... 2 pV/V 2 parts per trillion ! 2 ppt ! 2 × 10−12
A mass fraction of... 2 mg/kg 2 parts per million 2 ppm 2 × 10−6
A mass fraction of... 2 μg/kg 2 parts per billion ! 2 ppb ! 2 × 10−9
A mass fraction of... 2 ng/kg 2 parts per trillion ! 2 ppt ! 2 × 10−12
A mass fraction of... 2 pg/kg 2 parts per quadrillion ! 2 ppq ! 2 × 10−15
A volume fraction of... 5.2 μL/L 5.2 parts per million 5.2 ppm 5.2 × 10−6
A mole fraction of... 5.24 μmol/mol 5.24 parts per million 5.24 ppm 5.24 × 10−6
A mole fraction of... 5.24 nmol/mol 5.24 parts per billion ! 5.24 ppb ! 5.24 × 10−9
A mole fraction of... 5.24 pmol/mol 5.24 parts per trillion ! 5.24 ppt ! 5.24 × 10−12
A stability of... 1 (μA/A)/min 1 part per million per minute 1 ppm/min 1 × 10−6/min
A change of... 5 nΩ/Ω 5 parts per billion ! 5 ppb ! 5 × 10−9
An uncertainty of... 9 μg/kg 9 parts per billion ! 9 ppb ! 9 × 10−9
A shift of... 1 nm/m 1 part per billion ! 1 ppb ! 1 × 10−9
A strain of... 1 μm/m 1 part per million 1 ppm 1 × 10−6
A temperature coefficient of... 0.3 (μHz/Hz)/°C 0.3 part per million per °C 0.3 ppm/°C 0.3 × 10−6/°C
A frequency change of... 0.35 × 10−9 ƒ 0.35 part per billion ! 0.35 ppb ! 0.35 × 10−9

Note that the notations in the "SI units" column above are for the most part dimensionless quantities; that is, the units of measurement factor out in expressions like "1 nm/m" (1 nm/m =1 × 10−9) so the ratios are pure-number coefficients with values less than 1.

Uno (proposed dimensionless unit)

[edit]

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.[5] 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".[12] To date, the uno has not been adopted by any standards organization.

Footnotes

[edit]

See also

[edit]

References

[edit]
[edit]
Revisions and contributorsEdit on WikipediaRead on Wikipedia

Parts-per notation

View on Grokipedia
from Grokipedia
Parts-per notation refers to a system of expressing very small ratios or concentrations as "parts" of a substance relative to a total of one million (ppm), one billion (ppb), or one trillion (ppt), corresponding to multipliers of 10−610^{-6}, 10−910^{-9}, and 10−1210^{-12}, respectively. This notation is dimensionless and represents the proportion of a solute or component in a mixture, often without specifying the physical basis (such as mass, volume, or amount of substance) unless explicitly stated. It is commonly applied in fields like chemistry, environmental science, and engineering to denote trace amounts, such as pollutant levels in air or water. Despite its convenience for describing low concentrations—where, for example, 1 ppm equates to 1 milligram of solute per of solution in many contexts—the notation can lead to because "parts" may refer to different measurement scales. Authoritative bodies like NIST discourage the use of ppm, ppb, and ppt in formal documentation, permitting only the percent (%) symbol for relative values and advocating SI-compliant alternatives such as micrograms per liter (μg/L) or mole fractions. Similarly, IUPAC recommends avoiding ppm and related terms in and concentration expressions due to the need to clarify the basis of measurement, favoring explicit units like milligrams per (mg/kg) or micromoles per mole (μmol/mol). Common variants include parts per thousand (ppt or ‰, permille), used for slightly larger proportions like salinity in seawater. Overall, while widely used in regulatory and industrial contexts—such as EPA limits for —parts-per notation serves as a that must be interpreted carefully to ensure accuracy.

Fundamentals

Definition and Purpose

Parts-per notation refers to a system of pseudo-units employed in science and engineering to describe small values of dimensionless quantities, such as mass fractions or mole fractions, by expressing the proportion of one component relative to a large number of total parts, typically one million (ppm, or 10^{-6}) or one billion (ppb, or 10^{-9}). This notation simplifies the communication of trace-level concentrations that would otherwise require cumbersome decimal representations, such as 0.000001, by instead using whole numbers like 1 ppm. The primary purpose of parts-per notation is to facilitate the expression and interpretation of dilute mixtures or ratios in fields where precision for minute amounts is essential, avoiding the need for or long strings of zeros in everyday reporting. For instance, it is commonly applied to quantify trace contaminants in environmental samples or minor components in materials, making complex data more accessible without altering the underlying proportional meaning. Mathematically, for concentrations expressed on a mass basis, parts per million is defined as the mass of the solute divided by the total of the solution, multiplied by 10^6: ppm (by mass)=(mass of solutemass of solution)×106\text{ppm (by mass)} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 10^6 This yields a dimensionless value equivalent to micrograms of solute per gram of solution. An everyday example is the fluoride concentration in , where levels around 1 ppm—equivalent to 1 milligram of per liter—help prevent while remaining safe for consumption.

Historical Development

The use of ratio expressions for dilute concentrations originated in 19th-century chemistry, with early quantitative analyses laying the groundwork for later notations. In , the notation gained traction for trace gases in the mid-20th century, notably with Charles David Keeling's initiation of continuous CO₂ measurements at in 1958, reporting concentrations in parts per million (ppm) and establishing the as a benchmark for atmospheric monitoring. Adoption of parts-per notation expanded significantly in following the , propelled by growing awareness of and regulatory frameworks such as the U.S. Clean Air Act of 1970, which established expressed in ppm for criteria pollutants like and . This period marked a shift from sporadic, concentration reporting to more consistent use in policy and science, facilitating comparisons of trace pollutant levels across regions. By the 1970s, as analytical techniques improved sensitivity, the notation extended to (ppb) for even lower concentrations, such as in assessments of and water contaminants under the Clean Water Act of 1972. The evolution toward semi-standardized forms culminated in international guidelines, including the International Union of Pure and Applied Chemistry (IUPAC) Quantities, Units and Symbols in Physical Chemistry (Green Book, 2nd edition, 1993), which recognized ppm and related terms as non-SI units for approximate dimensionless quantities like or fractions at 10⁻⁶, while advising their use only when context clarifies the basis (e.g., ppm by or ) and preferring SI-derived alternatives for precision. These recommendations reflected ongoing efforts to address ambiguities in the notation's application across disciplines.

Expressions and Conventions

Common Parts-per Units

The primary parts-per units employed in scientific and technical contexts are parts per million (ppm), equivalent to one part in 1,000,000 or 10−610^{-6}; parts per billion (ppb), equivalent to 10−910^{-9}; and parts per trillion (ppt), equivalent to 10−1210^{-12}. These units are widely used to express trace concentrations in fields such as and chemistry. Less common variants include the permyriad (‱\text{‱}), which denotes one part in 10,000 or 10−410^{-4}, and the percent (%), a related but distinct form representing one part in 100 or 10−210^{-2}. The permyriad is occasionally applied in precise financial or metrological calculations but sees limited scientific adoption compared to ppm. These units maintain simple equivalences based on powers of 10, facilitating conversions across scales. For instance, 1 ppm equals 1,000 ppb or 1,000,000 ppt. The following table summarizes key decimal conversions:
UnitDecimal EquivalentRelation to ppm
ppm10−610^{-6}1 ppm
ppb10−910^{-9}0.001 ppm
ppt10−1210^{-12}10−610^{-6} ppm
permyriad (‱\text{‱})10−410^{-4}100 ppm
percent (%)10−210^{-2}10,000 ppm
In practice, ppm typically defaults to a mass/mass basis (e.g., milligrams per kilogram) unless otherwise specified, such as in gaseous mixtures where ppmv denotes parts per million by volume. This convention helps avoid ambiguity in concentration reporting, though explicit qualifiers like ppmv are recommended for clarity in volume-based applications.

Scaling and Numerical Representations

Parts-per notation employs scaling conventions that align with large powers of ten to represent trace amounts efficiently. The most common scales use a denominator of one million (10^6) for parts per million (ppm), one billion (10^9, following the short scale convention prevalent in scientific and American English contexts) for parts per billion (ppb), and one trillion (10^12, also short scale) for parts per trillion (ppt). These denominators facilitate the expression of very small ratios without cumbersome decimals, though the NIST Guide to the SI recommends preferring explicit powers of ten (e.g., 10^{-6} instead of ppm) to avoid ambiguities arising from varying definitions of "billion" and "trillion" in different languages. Numerical representations in parts-per notation directly correspond to decimal fractions of the whole. For example, a concentration of 500 ppm equals 500 parts in one million, or a decimal value of 0.0005, which can also be written as 5×10−45 \times 10^{-4}. Conversions between scales maintain this proportional relationship; notably, 1% (or 0.01 in ) is equivalent to ppm, as [10−2](/page/10+2)=104×10−6[10^{-2}](/page/10+2) = 10^4 \times 10^{-6}. In practice, parts-per values are frequently formatted using for clarity, especially when integrating with other quantitative data. A value of 25 ppb, for instance, translates to 25×10−925 \times 10^{-9}, or more compactly 2.5×10−82.5 \times 10^{-8}. This approach is particularly useful in fields requiring precise logarithmic scaling. For ultra-low concentrations below the ppb level (sub-10^{-9}), notation shifts to ppt or even smaller scales like parts per quadrillion (ppq, 10^{-15}) to accommodate detections in modern analytics, such as (ICP-MS), which can resolve contaminants at parts-per-trillion or lower thresholds.

Applications

Environmental and Health Contexts

In environmental monitoring, parts-per notation is essential for quantifying trace levels of pollutants that pose risks to ecosystems and human health. For air quality, the U.S. Environmental Protection Agency (EPA) establishes the National Ambient Air Quality Standard for ground-level ozone at 0.070 parts per million (ppm), equivalent to 70 parts per billion (ppb), measured as the fourth-highest 8-hour daily maximum concentration averaged over three years. In water quality assessments, the World Health Organization (WHO) sets a provisional guideline value of 10 micrograms per liter (µg/L) for lead in drinking water, corresponding to 10 ppb, to prevent adverse effects from chronic exposure. These standards enable precise tracking of contaminants at concentrations far below 1%, aiding in the enforcement of protective measures. Health applications leverage parts-per notation to define safe thresholds for toxins and intoxicants in biological media. Blood alcohol concentration (BAC) limits for legal driving, such as 80 mg/dL in numerous U.S. states and countries, translate to 0.08% by volume or 800 ppm, marking the point where impairment significantly affects judgment and coordination. Similarly, the U.S. (FDA) applies an action level of 100 ppb (0.1 ppm) for inorganic in infant rice cereals, based on risk assessments showing potential developmental risks at higher exposures. This notation allows clinicians and regulators to communicate minute yet critical levels effectively. Regulatory frameworks worldwide incorporate parts-per units to standardize impurity controls and global monitoring. The European Union's REACH regulation requires notification for articles containing substances of very high concern (SVHC) above 0.1% weight by weight (w/w), or 1,000 ppm, to ensure transparency in chemical supply chains. For atmospheric composition, organizations like the (NOAA) report (CO₂) concentrations in ppm, with global averages exceeding 400 ppm since 2016, reaching an annual average of about 423 ppm as of 2025, highlighting the scale of accumulation. The adoption of parts-per notation in these domains provides a streamlined way to interpret and compare ultra-low concentrations, enhancing risk communication for levels typically under 1% and supporting rapid decision-making in policy and public health.

Industrial and Scientific Uses

In industrial manufacturing, parts-per notation is essential for specifying material purity, particularly in alloys where trace impurities can significantly affect performance. For instance, 99.99% pure gold contains 100 ppm of impurities, ensuring the metal's conductivity and resistance to tarnishing in electronics and jewelry applications. Similarly, ultra-purity aluminum used in semiconductor production maintains impurity levels below 10 ppm to prevent defects in integrated circuits. In semiconductor fabrication, doping involves introducing controlled concentrations of elements like to alter electrical properties, often at parts-per-billion (ppb) levels. A typical boron doping concentration of 10^15 atoms/cm³ equates to approximately 20 ppb in , enabling precise control of resistivity for transistors and diodes. This level of accuracy is critical for achieving the high purity required in modern chips, where total impurities in 9N silicon are limited to 1 ppb. Scientific analysis relies on parts-per notation to quantify trace substances in settings. In , techniques like (ICP-MS) detect isotopic impurities at parts-per-trillion (ppt) levels, allowing identification of rare isotopes in geochemical and nuclear samples. In , the International Council for Harmonisation (ICH) M7 guidelines stipulate control of mutagenic impurities in drugs with an acceptable intake of 1.5 µg/day, corresponding to 1.5 ppm for a typical daily dose of 1 g, to minimize carcinogenic risk. Process control in industries uses parts-per notation for . In fuel production, a 10% ethanol blend in (E10) corresponds to 100,000 ppm by volume, standardizing additives for enhancement and emissions reduction. In , parts-per-million limits ensure compliance with purity standards during synthesis and formulation, preventing batch failures. The precision of ppm and ppb notations aligns with the detection capabilities of analytical instruments, facilitating reliable measurements in these fields. Gas chromatography-mass spectrometry (GC-MS) achieves detection limits down to 10 ppb for volatile organics, supporting impurity profiling in complex matrices like alloys and fuels. This compatibility enables industries to monitor and maintain quality at trace levels essential for product integrity.

Criticisms and Limitations

Ambiguities in Scale and Naming

The parts-per notation is prone to ambiguities stemming from variations in numerical scales and inconsistent terminology, which can lead to significant misinterpretations in scientific and technical contexts. These issues arise primarily from historical differences in large-number naming conventions and overlapping abbreviations, complicating the precise communication of low concentrations. Authoritative bodies such as the National Institute of Standards and Technology (NIST) highlight that such ambiguities in number names contribute to the of parts-per units like ppm, ppb, and ppt in favor of explicit SI expressions. A key source of confusion is the divergence between the short scale and long scale systems for naming large numbers. In the short scale, adopted in the United States and now the international standard in most scientific literature, "billion" denotes 10910^9, so parts per billion (ppb) corresponds to a ratio of 10−910^{-9}. In contrast, the long scale, used historically in parts of Europe until the mid-20th century, defines "billion" as 101210^{12}, shifting ppb to 10−1210^{-12} and introducing a three-order-of-magnitude difference. This has resulted in errors when translating older European texts or reports into modern short-scale contexts, potentially altering interpretations of trace-level measurements by factors of 1,000. The Unified Code for Units of Measure (UCUM) explicitly deprecates "ppb" due to this international ambiguity in "billion." Comparable scale discrepancies affect even larger units, such as parts per (ppt). Under the long scale, "trillion" traditionally meant 101810^{18}, while the short scale uses 101210^{12}; early literature employing the former could thus cause concentrations to appear overstated by six orders of magnitude when read through a short-scale lens. Such historical variances persist in archival environmental and chemical analyses, underscoring the need for contextual verification in cross-referencing data. Naming conventions exacerbate these scale-related problems, particularly with abbreviations that serve multiple purposes. The term "ppt" is notably ambiguous, as it commonly signifies (‰, or ) in fields like —where is approximately 35 ppt—but also denotes parts per trillion (10−1210^{-12}) in atmospheric or contexts. This dual usage has prompted IUPAC to recommend avoiding "ppt" entirely to prevent errors in interdisciplinary work. For instance, in assessments, "ppt" aligns numerically with the symbol (‰), but its overlap with the trillion-scale meaning can confuse non-specialists, as seen in some reports. Similarly, "parts per thousand" (ppt or ‰) is occasionally conflated with (parts per hundred, or 10^{-2}), blurring distinctions in relative proportion discussions despite their shared "parts-per" structure. These ambiguities have manifested in practical errors, such as misreadings of levels in international reports where short-scale assumptions prevail.

Differences in Fraction Types

In parts-per notation, the fraction, often denoted as ppm_m or ppm by , is defined as the of the of the solute to the total of the solution, multiplied by 10^6. This unit is commonly applied in contexts involving solids and liquids, where variations are less critical, such as in analyzing trace contaminants in or . The , denoted as ppm_x or ppm by mole, represents the of the number of moles of the solute to the total number of moles in the mixture, also scaled by 10^6. It finds frequent use in gas mixtures and thermodynamic calculations, where molecular composition is key, as seen in for species like . , expressed as ppm_v or ppm by volume, is the of the volume of the solute to the total volume of the solution, multiplied by 10^6. This is particularly standard for gases or fully miscible liquids, such as measuring air pollutants where volume-based standards prevail, like levels in ambient air quality regulations. These fraction types are not interchangeable due to differences in density and molar mass, leading to conversion challenges; for instance, 1 ppm_v of CO2 in air does not equal 1 ppm_m because CO2's molar mass (44 g/mol) exceeds that of dry air (approximately 29 g/mol), resulting in roughly 1.5 ppm_m equivalent under standard conditions. Such discrepancies can cause errors in environmental assessments if the basis is unspecified. The International Union of Pure and Applied Chemistry (IUPAC) warns against ambiguity in parts-per notation by recommending explicit specification of the fraction type using subscripts (e.g., ppm_m) or, preferably, SI-compliant units like µg/kg for mass-based concentrations to prevent misinterpretation.

Alternatives and Reforms

SI-Compliant Notations

The (SI) recommends expressing concentrations as dimensionless fractions to ensure clarity and precision, particularly for small values that might otherwise rely on parts-per notation. For mass-based concentrations, the preferred unit is the mass fraction, denoted as kg/kg (or simply 1, being dimensionless). Similarly, uses mol/mol, and uses m³/m³, all representing ratios of the respective quantities in the solute to the total mixture. To handle very low concentrations, SI employs decimal prefixes with these fractional units, providing direct equivalents to parts-per scales without ambiguity. For instance, a mass fraction of 10 µg/kg corresponds to 10 parts per billion (ppb) by , as 1 µg/kg = 10^{-9} kg/kg. Likewise, 1 mg/kg equals 1 part per million (ppm) by , using the microgram (µg) and milligram (mg) prefixes for 10^{-6} and 10^{-3}, respectively. These notations extend to other s, such as nmol/mol for mole-based ppb. The Bureau International des Poids et Mesures (BIPM) and the International Union of Pure and Applied Chemistry (IUPAC), in their updated guidelines since the 3rd edition (2007, reprinted 2008) and reaffirmed in the 4th edition (2023) of the IUPAC Green Book and the 9th edition of the SI Brochure (2019), explicitly advocate for these fractional expressions over parts-per terms in metrological contexts to avoid interpretive errors. This preference stems from the need for rigorous in scientific measurements, where parts-per can imply varying bases (e.g., , mole, or ). These SI-compliant notations offer key advantages: they are inherently dimensionless, eliminating unit mismatches, and unambiguous in scale, as values like 1 × 10^{-6} (for ppm equivalents) directly convey the proportion without additional qualifiers. In practice, for a concentration of 5 µg/kg in , this is precisely 5 × 10^{-9} kg/kg, facilitating consistent international comparisons. While types (, mole, ) differ in application, the SI framework ensures their uniform expression as ratios.

Proposed Dimensionless Units

In response to the ambiguities and inconsistencies in parts-per notations, metrologists have proposed dedicated dimensionless units to standardize the expression of small fractions using SI prefixes. One prominent suggestion is the "uno," a special name for the unit one (symbol: u or U), intended to serve as the base for prefix-modified expressions of dimensionless quantities. This unit would equal 1, allowing combinations like micro-uno (μu) to represent 10^{-6}, thereby directly replacing terms such as parts per million (ppm). The proposal aims to integrate seamlessly with the while eliminating the need for ad hoc notations like percent or ppm, which lack formal unit status. The uno concept was first formally recommended in 1998 by T. J. Quinn and I. M. Mills, who argued that naming the unit for dimension-one quantities would enable clearer, prefix-based scaling for ratios in fields like trace analysis and . Building on this, René Dybkaer further advocated for the uno in 2004, emphasizing its utility for quantities of dimension one and proposing the lowercase 'u' to distinguish it in equations. The International Union of Pure and Applied Physics (IUPAP) considered the idea in its 1999 General Assembly report, noting that the uno could be prefixed to express fractions systematically, such as milli-uno (mu) for 10^{-3}. Despite these endorsements, including discussions by the International Committee for Weights and Measures (CIPM) Consultative Committee for Units (CCU), the uno has not been adopted by any major standards body as of 2025, remaining a conceptual rather than an official SI element. Comparatively, the uno aligns directly with parts-per scales: 1 ppm equals 1 μu, 1 ppb equals 1 nu (nano-uno), and 1% equals 1 cu (centi-uno). This equivalence facilitates transitions from legacy notations without altering numerical values. For larger scales, prefixes like kilo-uno (ku = 10^3 u) would represent 1000, or 100,000%, providing a universal framework for both and macro-fractions in scientific reporting. Proponents highlight this as key to universality, though implementation would require updating international standards like ISO 80000 to incorporate the uno without conflicting with existing SI principles for dimensionless quantities.

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