What is the primary purpose of the parts-per notation in science and engineering?

The parts-per notation is used to describe very small, dimensionless quantities, such as mole fraction or mass fraction. These notations provide a standardized way to express extremely low concentrations or proportions of substances or phenomena.

Why are parts-per notations considered dimensionless quantities?

Parts-per notations are considered dimensionless because they represent fractions or ratios of quantities that have the same units, causing the units to cancel out. For example, a mass fraction is expressed as grams per gram (g/g), resulting in a pure number without units.

What are the most commonly used parts-per notations and their corresponding values?

The most commonly used parts-per notations include parts-per-million (ppm) representing 10 -6 , parts-per-billion (ppb) representing 10 -9 , parts-per-trillion (ppt) representing 10 -12 , and parts-per-quadrillion (ppq) representing 10 -15 .

Is the parts-per notation formally recognized by the International System of Units (SI)?

No, the parts-per notation is not formally part of the International System of Units (SI). While organizations like the International Bureau of Weights and Measures (BIPM) acknowledge its use, it is not an official SI unit.

In what scientific fields is parts-per notation frequently applied?

Parts-per notation is frequently used in fields such as chemistry, physics, and engineering. It is particularly common for describing dilute solutions, the relative abundance of substances, or proportional phenomena.

How is parts-per notation utilized when describing dilute solutions in chemistry?

In chemistry, parts-per notation is used to express the concentration of solutes in very dilute solutions. For instance, it can denote the mass of a pollutant per unit mass of a sample solution, like one-millionth of a gram per gram.

What common assumption allows for the equivalence between ppm and mg/L in aqueous solutions?

When working with aqueous solutions, it is commonly assumed that the density of water is approximately 1.00 g/mL. This assumption allows for the equivalence where 1 part per million (ppm) in mass fraction corresponds to 1 milligram per liter (mg/L) of solution.

Provide an example of how parts-per notation is used in physics or engineering.

In physics and engineering, parts-per notation can describe proportional phenomena like thermal expansion. For example, a metal alloy might expand 1.2 micrometers per meter for every degree Celsius, which can be expressed as a coefficient of thermal expansion of 1.2 ppm/°C.

How is parts-per notation used to express measurement accuracy or uncertainty?

Parts-per notation is employed to quantify the precision or uncertainty in measurements. For instance, the accuracy of a laser rangefinder might be stated as 1 millimeter per kilometer, which is equivalent to 1 ppm, indicating the error relative to the measured distance.

Explain the relationship between 'parts per hundred' and the percent symbol (%).

One part per hundred is generally represented by the percent symbol (%) and signifies one part in every 100 parts, equivalent to a value of 10 -2 . This is a widely understood notation for expressing proportions.

How is 'one part per thousand' typically represented, and what potential confusion exists?

One part per thousand is often spelled out in full to avoid confusion. While it can be denoted by the permille sign (‰), the abbreviation 'ppt' is sometimes used, which can be confused with 'parts per trillion,' although specific fields like oceanography may use 'ppt' for parts per thousand.

What is the symbol for 'one part per ten thousand,' and how common is its scientific usage?

One part per ten thousand is denoted by the permyriad sign (‱). Although it has an unambiguous value of 10 -4 , it is rarely used in science, with ppm typically being preferred instead.

What does 'per cent mille' (pcm) represent, and in which disciplines is it commonly used?

Per cent mille (pcm) represents one part per 100,000 (10 -5 ). It is commonly used in fields like epidemiology for prevalence rates (e.g., mortality, disease) and in nuclear reactor engineering as a unit of reactivity.

What does one part per million (ppm) signify, and how is it expressed in mining?

One part per million (ppm) signifies one part in 1,000,000 (10 -6 ). In mining, it is often used equivalently to express concentration as one gram per metric ton (g/t).

What is the magnitude represented by one part per billion (ppb)?

One part per billion (ppb) represents one part in 1,000,000,000 (10 -9 ). This signifies an extremely small fraction, equivalent to about three seconds within a century.

What does one part per trillion (ppt) represent, and what is its temporal equivalent?

One part per trillion (ppt) represents one part in 1,000,000,000,000 (10 -12 ). This extremely small ratio is equivalent to about thirty seconds over a span of one million years.

What does one part per quadrillion (ppq) represent, and where might measurements at this level be encountered?

One part per quadrillion (ppq) represents one part in 1,000,000,000,000,000 (10 -15 ). While relatively uncommon, measurements at the ppq level are sometimes performed, for example, in environmental analysis.

What is the primary criticism regarding the use of 'ppb' and 'ppt' notations?

The primary criticism regarding 'ppb' and 'ppt' is their ambiguity due to the use of different number scales ('long' and 'short' scales) for naming large numbers in different countries. This can lead to misunderstandings, prompting organizations like BIPM and NIST to discourage their use.

What ambiguity arises concerning the abbreviation 'ppt'?

The abbreviation 'ppt' can be ambiguous because it usually stands for 'parts per trillion,' but it occasionally refers to 'parts per thousand.' Context is necessary to determine its intended meaning unless explicitly defined.

What is a key issue with parts-per notation concerning different types of fractions?

A significant issue is that parts-per notation can refer to mass fraction, mole fraction, or volume fraction without explicit differentiation. This ambiguity is problematic because these different fractions can yield substantially different numerical values, especially for gases.

How can the ambiguity between mass, mole, and volume fractions be mitigated when using parts-per notation?

To avoid ambiguity, it is recommended to explicitly state the type of fraction being used, such as 'kg/kg' for mass fraction, 'mol/mol' for mole fraction, or 'm³/m³' for volume fraction, even though they are all dimensionless.

What suffixes are sometimes used to specify volume fraction in parts-per notation, and what is their typical meaning?

The suffixes 'V' or 'v' are sometimes appended to parts-per notation (e.g., ppmV, ppbv, pptv) to indicate volume fraction. However, these are often used to denote mole fractions, with 'volume fraction' itself being less common except in specific contexts like alcohol by volume.

What does the suffix 'w' signify when added to parts-per notation abbreviations?

The suffix 'w' (standing for 'weight') is sometimes added to parts-per notation abbreviations, such as ppmw or ppbw, to explicitly denote mass fraction and distinguish it from volume or mole fractions.

Why does the usage of parts-per notation vary across different scientific disciplines?

The usage varies because each discipline often adopts conventions that are practical for its specific applications. This leads to inconsistencies, where a researcher might assume their specific usage (e.g., mass/mass) is universally correct and fail to specify it, causing misinterpretation by others.

Provide examples of how different fields use parts-per notation differently.

For example, electrochemists often use volume/volume, while chemical engineers might use mass/mass or volume/volume. Chemists, occupational safety experts, and those dealing with permissible exposure limits frequently use mass/volume, highlighting the need for explicit clarification in publications.

What are SI-compliant expressions that can be used as alternatives to parts-per notation?

SI-compliant expressions include using standard SI units where the units cancel out, such as cm/m for strain, mV/V for sensitivity, or mg/kg for mass fraction. These explicitly show the ratio and are considered more precise alternatives by standards organizations.

Which parts-per notations are explicitly not recognized by the BIPM for use with the SI?

The BIPM explicitly does not recognize notations like permille (‰), permyriad (‱), parts per billion (ppb), and parts per trillion (ppt) as suitable for denoting dimensionless quantities within the SI system, although percent (%) is sometimes accepted in mathematical expressions.

How is a strain of 2 cm/m represented using SI-compliant units and parts-per notation?

A strain of 2 cm/m is represented using SI units as 2 cm/m. In parts-per notation, this corresponds to 2 parts per hundred, which is symbolized as 2%.

How is a mass fraction of 2 mg/kg represented using SI-compliant units and parts-per notation?

A mass fraction of 2 mg/kg is represented using SI units as 2 mg/kg. In parts-per notation, this is equivalent to 2 parts per million, symbolized as 2 ppm.

What was the 'uno' proposal, and what was its outcome?

In 1999, the International Union of Pure and Applied Physics (IUPAP) proposed adopting a special name, 'uno' (symbol: U), to represent the number 1 for dimensionless quantities. However, the proposal received a largely negative response and was ultimately dropped, with 'uno' not being adopted by any standards organization.

According to the source, what is the accuracy specification for a laser rangefinder that might read '±(1 mm + 1 ppm)'?

The accuracy specification '±(1 mm + 1 ppm)' for a laser rangefinder means that the measurement includes a fixed error of ±1 mm plus an error proportional to the distance measured, equal to 1 ppm (one part per million). Therefore, for very short distances, the ±1 mm component dominates, while for longer distances, the ppm component becomes more significant.

How does the conversion factor for the coefficient of thermal expansion change when using Fahrenheit instead of Celsius?

When converting the coefficient of thermal expansion from Celsius to Fahrenheit, the numerical value changes because a Fahrenheit-degree interval is smaller than a Celsius-degree interval (5/9). For example, a value might be expressed as 18.7 (µin/in)/°C, which converts to approximately 10.4 (µin/in)/°F.

What are the common abbreviations for parts-per notation and their corresponding powers of ten?

The common abbreviations and their corresponding powers of ten are: ppm (parts-per-million) for 10 -6 , ppb (parts-per-billion) for 10 -9 , ppt (parts-per-trillion) for 10 -12 , and ppq (parts-per-quadrillion) for 10 -15 .

What is the meaning of the image caption showing Fluorescein solutions?

The image caption describes Fluorescein aqueous solutions diluted from 10,000 parts per million (ppm) down to 1 ppm in ten-fold intervals. It notes the color changes from deep red at 10,000 ppm to orange, then vibrant yellow, and finally a very pale yellow at 1 ppm, illustrating the effect of concentration.

What does the image visualizing parts per block illustrate?

The image visually represents the relative magnitudes of 1%, 1‰ (per mille), 1‱ (per ten thousand), 1 pcm (per cent mille), and 1 ppm (per million) as fractions of a large block, helping to understand the scale differences between these notations.

What is the significance of the red exclamation mark next to certain notations in the SI-compliant expressions table?

The red exclamation mark (!) next to certain notations, such as ‰, ‱, ppb, and ppt, indicates that these specific parts-per notations are explicitly not recognized by the International Bureau of Weights and Measures (BIPM) as suitable for denoting dimensionless quantities within the SI system.

What is the common interpretation of parts-per notations when used in regular prose?

When used in regular prose, parts-per notations, like '2 ppb,' are generally interpreted as a comparative ratio, meaning 'two parts in a billion parts,' rather than strictly adhering to mathematical unit cancellation.

What is the temporal equivalent of one part per billion (ppb)?

One part per billion is equivalent to approximately three seconds out of a century.

What is the temporal equivalent of one part per trillion (ppt)?

One part per trillion is equivalent to approximately thirty seconds out of every million years.

What is the temporal equivalent of one part per quadrillion (ppq)?

One part per quadrillion is equivalent to approximately two and a half minutes out of the age of the Earth (4.5 billion years).

What is the meaning of 'ppm/min' as seen in the SI-compliant expressions table?

'ppm/min' signifies 'parts per million per minute.' It is used to express a rate of change, such as the stability or drift of a measurement over time, indicating how much the quantity changes in parts per million for each minute that passes.

What is the purpose of the 'See also' section in the article?

The 'See also' section provides links to related concepts, units, and organizations that are relevant to parts-per notation, such as Percentage (%), Permille (‰), Permyriad (‱), Per cent mille (pcm), and the Per-unit system, offering further avenues for exploration.

What external resources are provided for further information on parts-per notation?

The article provides links to Wiktionary for definitions of ppm, ppb, ppt, and ppq, Wikimedia Commons for related media, and the official websites of the National Institute of Standards and Technology (NIST) and the International Bureau of Weights and Measures (BIPM).

What is the role of the International Bureau of Weights and Measures (BIPM) concerning parts-per notation?

The BIPM recognizes the practical use of parts-per notation but does not consider it formally part of the SI. It advises against using 'ppb' and 'ppt' due to ambiguity related to number scales and suggests using SI-compliant expressions instead for clarity.

What is the stance of the U.S. National Institute of Standards and Technology (NIST) on language-dependent terms in measurements?

NIST takes a stringent position, stating that language-dependent terms like 'billion' and 'trillion' (which affect ppb and ppt) are not acceptable for use with the SI system when expressing the values of quantities.

How is 'parts per million' (ppm) used in the context of mining?

In mining, 'ppm' is often used as an equivalent measure for concentration, specifically representing one gram per metric ton (g/t).

What is the significance of the footnote regarding dioxin measurements?

The footnote highlights that measurements for substances like dioxin are routinely performed at extremely low levels, even below parts per quadrillion (ppq). It mentions regulatory limits and historical recommendations by the U.S. EPA, illustrating the need for highly sensitive measurement techniques and notations like ppq.

Parts-per Notation Wiki: Quantifying the Infinitesimal: A Deep Dive into Parts-per Notation

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Introduction

Defining Parts-per Notation

In the rigorous domains of science and engineering, the parts-per notation serves as a standardized framework for expressing exceedingly small dimensionless quantities. These notations are crucial for quantifying minute concentrations, ratios, or proportions, such as mole fractions or mass fractions, where absolute values are impractical or lack context.^[a] As these are essentially quantity-per-quantity measures, they are inherently pure numbers, devoid of specific units of measurement.

Common Notations

Several common parts-per notations are widely employed:

Parts-per-million (ppm): Represents 10⁻⁶, or one part in a million.
Parts-per-billion (ppb): Represents 10⁻⁹, or one part in a billion.
Parts-per-trillion (ppt): Represents 10⁻¹², or one part in a trillion.
Parts-per-quadrillion (ppq): Represents 10⁻¹⁵, or one part in a quadrillion.

It is imperative to note that this notation system is not formally integrated into the International System of Units (SI) and can sometimes lead to ambiguity.

Visualizing Dilution

Consider the visual representation of fluorescein solutions. As concentrations decrease through ten-fold dilutions, the vibrant yellow color of a 1 ppm solution becomes progressively fainter, transitioning from orange to deep red at 10,000 ppm. This illustrates how parts-per notation effectively describes minute quantities relative to a whole.

Applications Across Disciplines

Environmental Science

In environmental monitoring, parts-per notation is indispensable for describing the concentration of dissolved substances in water, such as minerals or pollutants. For instance, "1 ppm" might signify one-millionth of a gram of a pollutant per gram of water sample. Given the density of water is approximately 1 g/mL, this often translates to 1 milligram per liter (mg/L).

Physics and Engineering

These notations are also prevalent in physics and engineering. For example, the thermal expansion of a metal alloy might be expressed as 1.2 micrometers per meter per degree Celsius, denoted as 1.2 ppm/°C. Similarly, the precision of measurement instruments, like a laser rangefinder with an accuracy of 1 millimeter per kilometer, is effectively communicated as 1 ppm.

Analytical Chemistry

In fields like nuclear magnetic resonance (NMR) spectroscopy, chemical shifts are commonly reported in ppm. This unit provides a field-strength-independent measure, representing the difference in frequency relative to a reference standard, typically expressed in Hertz (Hz) divided by the spectrometer's operating frequency in Megahertz (MHz).

Understanding Parts-per Expressions

Relative Proportions

Parts-per notations fundamentally represent relative proportions. Whether expressed as mass fraction, mole fraction, or volume fraction, the underlying principle is a ratio where units cancel out, resulting in a dimensionless coefficient. For instance, 2 nanometers per meter (2 nm/m) simplifies to 2 x 10⁻⁹, equivalent to 2 ppb.

The following table illustrates the relationships between various parts-per expressions:

Parts-per Equivalencies
1 of → = ↧ of ↓	per cent (%)	per mille (‰)	per 10,000 (‱)	per 100,000 (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	10⁻⁴
ppm	10,000	1,000	100	10	1	0.001
ppb	10⁷	10⁶	10⁵	10,000	1,000	1

Note: The table uses the short scale for 'billion' (10⁹) and 'trillion' (10¹²).

Temporal and Spatial Equivalents

These notations can be contextualized with temporal or spatial equivalents to aid comprehension:

One percent (%) is roughly equivalent to fourteen minutes out of a day.
One part per thousand (‰) is approximately ninety seconds out of a day.
One part per ten thousand (‱) equates to about nine seconds out of a day.
One part per hundred thousand (pcm) is roughly five minutes out of a year, or 1 cm of error per km.
One part per million (ppm) is approximately 32 seconds out of a year, or 1 mm of error per km.
One part per billion (ppb) is equivalent to about three seconds out of a century.
One part per trillion (ppt) represents about thirty seconds over a million years.
One part per quadrillion (ppq) is approximately two and a half minutes over the age of the Earth.

Critiques and Ambiguities

Lack of Formal SI Integration

While the International Bureau of Weights and Measures (BIPM) acknowledges parts-per notation, it is not formally part of the SI. The BIPM and ISO permit the use of the percent symbol (%) with SI for dimensionless quantities, but the usage of ppb and ppt is discouraged due to potential confusion arising from differing interpretations of "billion" and "trillion" across language scales (long vs. short scales).^[BIPM-2]

Thousand vs. Trillion Confusion

A significant point of contention is the potential ambiguity of "ppt". While predominantly understood as "parts per trillion," it is occasionally misused to mean "parts per thousand." Context is therefore crucial for accurate interpretation, necessitating explicit definition in technical communication.^{[citation needed]}

Mass, Mole, or Volume?

Another critical issue is the lack of specificity regarding the type of fraction being represented. Parts-per notation can refer to mass fraction (e.g., mg/kg), mole fraction (mol/mol), or volume fraction (e.g., µL/L). Without explicit clarification (e.g., using suffixes like 'w' for weight or 'v' for volume, or stating units like kg/kg), misinterpretation is highly probable, particularly in fields like atmospheric chemistry where these distinctions are significant.^[9]

SI-Compliant Alternatives

Preferred Expressions

To mitigate ambiguity, SI-compliant expressions are recommended. These explicitly state the ratio of units, ensuring clarity. For example, a strain of 1 micrometer per meter (1 µm/m) is unambiguously 1 ppm. Similarly, a mass fraction of 2 milligrams per kilogram (2 mg/kg) is clearly 2 ppm.

The following table contrasts parts-per notations with their SI-compliant counterparts:

SI-Compliant Expressions for Dimensionless Quantities
Measure Example	SI Units	Parts-per Notation	Value (Scientific Notation)
A strain of...	2 cm/m	2%	2 × 10⁻²
A sensitivity of...	2 mV/V	2 ‰ (Discouraged)	2 × 10⁻³
A sensitivity of...	0.2 mV/V	2 ‱ (Discouraged)	2 × 10⁻⁴
A sensitivity of...	2 µV/V	2 ppm	2 × 10⁻⁶
A sensitivity of...	2 nV/V	2 ppb (Discouraged)	2 × 10⁻⁹
A sensitivity of...	2 pV/V	2 ppt (Discouraged)	2 × 10⁻¹²
A mass fraction of...	2 mg/kg	2 ppm	2 × 10⁻⁶
A mass fraction of...	2 µg/kg	2 ppb (Discouraged)	2 × 10⁻⁹
A mass fraction of...	2 ng/kg	2 ppt (Discouraged)	2 × 10⁻¹²
A mass fraction of...	2 pg/kg	2 ppq (Discouraged)	2 × 10⁻¹⁵
A volume fraction of...	5.2 µL/L	5.2 ppm	5.2 × 10⁻⁶
A mole fraction of...	5.24 µmol/mol	5.24 ppm	5.24 × 10⁻⁶
A stability of...	1 (µA/A)/min	1 ppm/min	1 × 10⁻⁶/min
A change of...	5 nΩ/Ω	5 ppb (Discouraged)	5 × 10⁻⁹
An uncertainty of...	9 µg/kg	9 ppb (Discouraged)	9 × 10⁻⁹
A shift of...	1 nm/m	1 ppb (Discouraged)	1 × 10⁻⁹
A strain of...	1 µm/m	1 ppm	1 × 10⁻⁶
A temperature coefficient of...	0.3 (µHz/Hz)/°C	0.3 ppm/°C	0.3 × 10⁻⁶/°C

Note: Entries marked "(Discouraged)" highlight notations that the BIPM advises against using due to potential ambiguity.

Clarity in Communication

While parts-per notations remain prevalent due to their convenience, especially in established fields, the scientific community increasingly emphasizes the use of explicit SI units (e.g., mg/kg, mol/mol, m³/m³) or clearly defined parts-per expressions to ensure precision and avoid misinterpretation across different disciplines and international contexts.

Proposed Units: The "Uno"

A Novel Concept

Recognizing the challenges associated with expressing dimensionless quantities, the International Union of Pure and Applied Physics (IUPAP) proposed the adoption of a special name, "uno" (symbol: U), in 1999. This unit was intended to represent the numerical value '1' for dimensionless quantities, simplifying expressions that currently rely on parts-per notation or explicit unit ratios.

Limited Adoption

Despite the proposal's intent to streamline scientific communication, the "uno" unit faced significant resistance. A subsequent report to the International Committee for Weights and Measures (CIPM) indicated overwhelmingly negative responses, leading to the recommendation to abandon the idea. Consequently, the "uno" has not been adopted by any major standards organization and remains largely a theoretical concept.

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References

NIST: Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt.

A full list of references for this article are available at the Parts-per notation Wikipedia page

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This educational resource was generated by Artificial Intelligence, drawing upon information from publicly available sources, primarily Wikipedia. While efforts have been made to ensure accuracy and clarity, the content is intended for informational and educational purposes only. It may not encompass the entirety of the subject matter or reflect the most current data.

This content does not constitute professional advice. The information presented herein is not a substitute for expert consultation in fields such as chemistry, physics, engineering, or metrology. Users should always consult official documentation and qualified professionals for specific applications or interpretations. Reliance on any information provided on this website is solely at the user's own risk.

The creators of this page assume no responsibility for any errors, omissions, or consequences arising from the use of the information contained herein.

Quantifying the Infinitesimal

💡 Dive in with Flashcard Learning! 💡

Introduction ℹ️

📏 Defining Parts-per Notation

🔢 Common Notations

🧪 Visualizing Dilution

Applications Across Disciplines 🔬

💧 Environmental Science

⚙️ Physics and Engineering

⚛️ Analytical Chemistry

Understanding Parts-per Expressions 📊

⚖️ Relative Proportions

⏳ Temporal and Spatial Equivalents

Critiques and Ambiguities ⚠️

🗣️ Lack of Formal SI Integration

🤔 Thousand vs. Trillion Confusion

⚖️ Mass, Mole, or Volume?

SI-Compliant Alternatives ✅

➡️ Preferred Expressions

💡 Clarity in Communication

Proposed Units: The "Uno" 💡

🚀 A Novel Concept

📉 Limited Adoption

Teacher's Corner 🧑‍🏫

Edit and Print this course in the Wiki2Web Teacher Studio

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References

📜 References

Feedback & Support 👍

To report an issue with this page, or to find out ways to support the mission, please click here.

Disclaimer ⚠️

📜 Important Notice

Dive in with Flashcard Learning!

Introduction

Defining Parts-per Notation

Common Notations

Visualizing Dilution

Applications Across Disciplines

Environmental Science

Physics and Engineering

Analytical Chemistry

Understanding Parts-per Expressions

Relative Proportions

Temporal and Spatial Equivalents

Critiques and Ambiguities

Lack of Formal SI Integration

Thousand vs. Trillion Confusion

Mass, Mole, or Volume?

SI-Compliant Alternatives

Preferred Expressions

Clarity in Communication

Proposed Units: The "Uno"

A Novel Concept

Limited Adoption

Teacher's Corner

True or False?

Test Your Knowledge!

Gamer's Corner

Discover other topics to study!

References

Feedback & Support

Disclaimer

Important Notice