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Parts-per notations are considered dimensionless because they represent ratios of quantities with different units.
Answer: False
The source clarifies that parts-per notations are dimensionless because they represent ratios of quantities with the *same* units, which cancel out, not different units.
Parts-per notation is primarily used for expressing large quantities or concentrations.
Answer: False
Parts-per notation is specifically designed for expressing very small, dimensionless quantities, such as extremely low concentrations or proportions, not large quantities.
What is the primary function of parts-per notation in science and engineering?
Answer: To describe very small, dimensionless quantities like concentrations or proportions.
Parts-per notation serves as a standardized method for expressing extremely small, dimensionless quantities, such as concentrations, proportions, or ratios, which are common in scientific and engineering contexts.
Why are parts-per notations considered dimensionless quantities?
Answer: Because they represent ratios where the numerator and denominator have the same units, causing cancellation.
Parts-per notations are inherently dimensionless because they are formed by the ratio of two quantities possessing identical units. This unit cancellation results in a pure numerical value, independent of any specific unit of measurement.
Parts-per-million (ppm) represents a quantity of 10<sup>-6</sup>.
Answer: True
Parts-per-million (ppm) signifies one part in one million, corresponding to a value of 10<sup>-6</sup>.
The percent symbol (%) represents one part per thousand.
Answer: False
The percent symbol (%) signifies one part per hundred (10<sup>-2</sup>), not one part per thousand. One part per thousand is represented by the permille symbol (‰).
The permyriad sign (‱) is a commonly used notation for one part in ten thousand.
Answer: False
While the permyriad sign (‱) denotes one part in ten thousand (10<sup>-4</sup>), it is rarely used in scientific practice, with parts-per-million (ppm) being more commonly preferred.
Per cent mille (pcm) represents one part per 100,000.
Answer: True
Per cent mille (pcm) signifies one part per 100,000 (10<sup>-5</sup>) and is frequently employed in fields such as epidemiology and nuclear reactor engineering.
The permille sign (‰) is often spelled out to avoid confusion with other notations.
Answer: True
To ensure clarity and prevent confusion with abbreviations like 'ppt' (parts per trillion), the permille notation (‰) is frequently spelled out in full as 'per thousand'.
Which of the following is NOT among the most commonly used parts-per notations mentioned in the source?
Answer: parts-per-ten-thousand (pp10k)
While parts-per-million (ppm), parts-per-billion (ppb), and parts-per-trillion (ppt) are frequently encountered, parts-per-ten-thousand (pp10k) is not typically listed among the most common notations, although it has a defined value (10<sup>-4</sup>).
What is the value represented by parts-per-billion (ppb)?
Answer: 10<sup>-9</sup>
Parts-per-billion (ppb) represents one part in one billion, corresponding to a value of 10<sup>-9</sup>.
How is 'one part per hundred' typically represented?
Answer: As %
The notation for 'one part per hundred' is the percent symbol (%), representing a value of 10<sup>-2</sup>. This is a universally recognized representation for proportions out of one hundred.
Which notation represents one part per thousand?
Answer: ‰
One part per thousand is represented by the permille symbol (‰), which signifies a value of 10<sup>-3</sup>. This notation is distinct from percent (%) and parts-per-trillion (ppt).
In aqueous solutions, 1 ppm is commonly assumed to be equivalent to 1 mg/L.
Answer: True
This equivalence is commonly assumed in aqueous solutions due to the approximation that the density of water is approximately 1.00 g/mL, allowing mass fraction (ppm) to be directly related to mass per volume (mg/L).
In mining, parts per million (ppm) is sometimes used interchangeably with grams per metric ton (g/t).
Answer: True
In the mining industry, the concentration unit 'grams per metric ton' (g/t) is frequently employed as an equivalent measure to parts per million (ppm) for expressing the abundance of elements or minerals.
The coefficient of thermal expansion conversion factor between Celsius and Fahrenheit is the same because both are degree measures.
Answer: False
The conversion factor for the coefficient of thermal expansion differs between Celsius and Fahrenheit because a degree interval on the Fahrenheit scale is smaller than on the Celsius scale (a factor of 5/9).
The notation 'ppm/min' is used to express a rate of change over time.
Answer: True
'ppm/min' signifies 'parts per million per minute,' indicating a rate of change, commonly used to describe drift or stability over time.
Measurements for substances like dioxin are routinely performed at levels below parts per quadrillion (ppq).
Answer: True
The analysis of certain substances, such as dioxins, frequently requires measurements at extremely low concentrations, extending down to levels below parts per quadrillion (ppq), necessitating highly sensitive detection methods.
In which scientific fields is parts-per notation commonly applied?
Answer: In fields like chemistry, physics, and engineering for dilute solutions and proportions.
Parts-per notation finds extensive application across various scientific disciplines, including chemistry, physics, environmental science, and engineering, particularly when dealing with dilute solutions, trace concentrations, and relative proportions.
What assumption allows for the common equivalence of 1 ppm and 1 mg/L in aqueous solutions?
Answer: The density of the solution is approximately 1.00 g/mL.
The common equivalence of 1 ppm (mass fraction) to 1 mg/L in aqueous solutions relies on the assumption that the solution's density is approximately 1.00 g/mL, which is characteristic of dilute aqueous solutions.
In the context of mining, what is often used equivalently to express concentration as 'ppm'?
Answer: Grams per metric ton (g/t)
In the mining industry, the concentration unit 'grams per metric ton' (g/t) is frequently employed as an equivalent measure to parts per million (ppm) for expressing the abundance of elements or minerals.
What does 'ppm/min' signify?
Answer: Parts per million per minute, indicating a rate of change.
'ppm/min' denotes 'parts per million per minute,' a unit used to express a rate of change over time, commonly applied to quantify drift or stability in measurements.
Why might the usage of parts-per notation vary across different scientific disciplines?
Answer: Because disciplines adopt conventions practical for their specific applications, leading to inconsistencies.
Variations in the usage of parts-per notation across disciplines arise because each field tends to adopt conventions that are most practical for its specific applications. This can lead to inconsistencies and potential misunderstandings if not explicitly clarified.
The parts-per notation is an officially recognized unit within the International System of Units (SI).
Answer: False
Parts-per notation is not formally recognized as an SI unit by the International System of Units, although its practical application is acknowledged by metrology bodies such as the BIPM.
The abbreviation 'ppt' unambiguously refers to 'parts per trillion' in all scientific contexts.
Answer: False
The abbreviation 'ppt' can be ambiguous, as it often signifies 'parts per trillion' but may also refer to 'parts per thousand' in specific contexts, necessitating careful attention to the defined meaning.
The primary criticism of 'ppb' and 'ppt' is their potential to be confused with parts per hundred.
Answer: False
The primary criticism of 'ppb' and 'ppt' stems from their ambiguity related to language-dependent number scales ('long' vs. 'short'), not confusion with 'parts per hundred'.
The suffixes 'V' or 'v' appended to parts-per notation always indicate volume fraction.
Answer: False
The suffixes 'V' or 'v' appended to parts-per notation, such as ppmV, typically indicate volume fraction, but are often used to denote mole fraction, highlighting a common point of ambiguity.
The International Union of Pure and Applied Physics (IUPAP) successfully proposed the adoption of 'uno' as a symbol for the number 1.
Answer: False
The proposal by IUPAP to adopt 'uno' as a symbol for the number 1 was met with significant negative feedback and was ultimately not adopted by international standards organizations.
The BIPM explicitly recognizes permille (‰) and permyriad (‱) as suitable for denoting dimensionless quantities within the SI system.
Answer: False
The BIPM explicitly does not recognize notations like permille (‰) and permyriad (‱) as suitable for denoting dimensionless quantities within the SI system, although '%' is sometimes accepted in mathematical contexts.
The U.S. National Institute of Standards and Technology (NIST) accepts language-dependent terms like 'billion' and 'trillion' for use with the SI system.
Answer: False
NIST explicitly states that language-dependent terms such as 'billion' and 'trillion' are not acceptable for use with the SI system when expressing the values of quantities, due to potential ambiguity.
The ambiguity in parts-per notation can arise because it may refer to mass fraction, mole fraction, or volume fraction without explicit differentiation.
Answer: True
This ambiguity is a significant concern, as parts-per notation does not inherently specify whether it represents mass fraction, mole fraction, or volume fraction, which can lead to substantially different numerical values, particularly for gaseous mixtures.
The proposal to adopt the symbol 'U' for 'uno' was widely accepted by international standards organizations.
Answer: False
The proposal by IUPAP to adopt 'uno' as a symbol for the number 1 was met with significant negative feedback and was ultimately not adopted by international standards organizations.
The International Bureau of Weights and Measures (BIPM) discourages the use of 'ppb' and 'ppt' due to potential ambiguity.
Answer: True
The BIPM advises against the use of 'ppb' and 'ppt' because their interpretation can vary based on language-dependent number scales ('long' vs. 'short'), leading to potential misunderstandings and ambiguity.
According to the source, is parts-per notation formally part of the International System of Units (SI)?
Answer: No, it is not formally part of the SI, although its use is acknowledged.
Parts-per notation is not formally incorporated into the International System of Units (SI). While widely used and acknowledged by metrology organizations, it does not hold official SI status.
What potential confusion exists with the abbreviation 'ppt'?
Answer: It can be confused with 'parts per thousand' in some contexts, despite usually meaning 'parts per trillion'.
The abbreviation 'ppt' presents a potential for confusion because, while commonly understood as 'parts per trillion,' it is sometimes used to denote 'parts per thousand' in specific fields, requiring contextual clarification.
What is the main reason cited for the ambiguity of 'ppb' and 'ppt' notations?
Answer: They rely on language-dependent number scales ('long' vs. 'short').
The primary source of ambiguity for 'ppb' and 'ppt' stems from their reliance on language-dependent number scales (e.g., the 'long scale' versus the 'short scale' for defining 'billion' and 'trillion'), leading to differing numerical interpretations.
The proposal by IUPAP to adopt the symbol 'uno' for the number 1 was ultimately:
Answer: Dropped due to a largely negative response.
The proposal by the International Union of Pure and Applied Physics (IUPAP) to introduce 'uno' (U) as a symbol for the number 1 was met with considerable opposition and was subsequently abandoned.
Which of the following notations is explicitly NOT recognized by the BIPM for use within the SI system?
Answer: Permille (‰)
The International Bureau of Weights and Measures (BIPM) explicitly does not recognize notations such as permille (‰), permyriad (‱), ppb, and ppt as suitable for denoting dimensionless quantities within the SI framework, although '%' is sometimes accepted in mathematical contexts.
What is the primary issue with using parts-per notation concerning different types of fractions (mass, mole, volume)?
Answer: The notation does not specify which type of fraction is being used, leading to ambiguity.
The primary issue is that parts-per notation often fails to explicitly differentiate between mass fraction, mole fraction, and volume fraction. This lack of specification can lead to significant ambiguity, as these fractions can yield numerically different values, especially in gaseous systems.
What is the significance of the red exclamation mark (!) next to certain notations in the SI-compliant expressions table?
Answer: It denotes that the notation is explicitly not recognized by BIPM for SI use.
The red exclamation mark (!) adjacent to specific notations in the SI-compliant table signifies that these parts-per notations are explicitly discouraged or not recognized by the BIPM for use within the SI system.
What is a potential issue with parts-per notation when applied to gases?
Answer: Mass, mole, and volume fractions can yield substantially different numerical values.
When applied to gases, parts-per notation can be problematic because mass fraction, mole fraction, and volume fraction may yield significantly different numerical values, exacerbating the inherent ambiguity of the notation if not explicitly defined.
What does the NIST stance on language-dependent terms imply for the use of 'ppb' and 'ppt'?
Answer: They are not acceptable for use with the SI system.
NIST's stance against language-dependent terms implies that 'ppb' and 'ppt' are not considered acceptable for use within the SI system due to their reliance on potentially ambiguous number scales, advocating instead for explicit SI-compliant expressions.
The suffix 'w' in notations like ppmw explicitly denotes mass fraction.
Answer: True
The suffix 'w', standing for 'weight', is sometimes appended to parts-per notation (e.g., ppmw) to explicitly signify mass fraction, thereby distinguishing it from other fraction types.
Which of the following suffixes is sometimes used to explicitly denote mass fraction in parts-per notation?
Answer: w
The suffix 'w', signifying 'weight', is occasionally appended to parts-per notation abbreviations (e.g., ppmw) to explicitly indicate mass fraction and differentiate it from volume or mole fractions.
How can the ambiguity between mass, mole, and volume fractions be mitigated when using parts-per notation?
Answer: By explicitly stating the type of fraction, e.g., 'kg/kg' or 'mol/mol'.
To mitigate ambiguity, it is best practice to explicitly state the type of fraction being represented, such as 'kg/kg' for mass fraction or 'mol/mol' for mole fraction, even though these are dimensionless quantities.
What does the suffix 'V' or 'v' sometimes appended to parts-per notation (e.g., ppmV) typically indicate?
Answer: Mole fraction, although sometimes used for volume fraction.
The suffixes 'V' or 'v' appended to parts-per notation, such as ppmV, are often intended to indicate mole fraction. However, they are sometimes ambiguously used to denote volume fraction as well.
Which of the following is an SI-compliant expression that can be used as an alternative to parts-per notation?
Answer: A ratio expressed using standard SI units where units cancel.
SI-compliant alternatives to parts-per notation include expressing quantities as ratios using standard SI units where units cancel (e.g., cm/m for strain, mg/kg for mass fraction), providing explicit clarity.
One part per trillion (ppt) is equivalent to approximately thirty seconds over a span of one million years.
Answer: True
This temporal analogy illustrates the minuscule scale of one part per trillion (10<sup>-12</sup>), equating it to roughly thirty seconds within a million-year period.
A strain of 2 cm/m is equivalent to 2 parts per million (ppm).
Answer: False
A strain of 2 cm/m represents 2 parts per hundred, which is equivalent to 2% (percent), not 2 parts per million (ppm).
The temporal equivalent of one part per billion (ppb) is approximately three seconds out of a century.
Answer: True
This temporal analogy illustrates the minuscule scale of one part per billion (10<sup>-9</sup>), equating it to approximately three seconds within a century.
The 'parts per block' image visually demonstrates the relative magnitudes of different parts-per notations.
Answer: True
The 'parts per block' visualization effectively illustrates the comparative scales of various parts-per notations, such as percent, permille, and parts-per-million, aiding in conceptual understanding.
The temporal equivalent of one part per quadrillion (ppq) is roughly two and a half minutes over the age of the Earth.
Answer: True
This temporal analogy highlights the extreme minuteness of one part per quadrillion (10<sup>-15</sup>), equating it to approximately two and a half minutes within the entire age of the Earth.
The accuracy specification '±(1 mm + 1 ppm)' for a laser rangefinder means the error is solely dependent on the distance measured.
Answer: False
This accuracy specification indicates a combined error: a fixed component of ±1 mm plus a distance-dependent component of ±1 ppm. The total error is thus a function of both the fixed offset and the measured distance.
The image caption showing Fluorescein solutions illustrates color changes related to concentration.
Answer: True
The caption accompanying the Fluorescein solutions describes how varying concentrations, from 10,000 ppm down to 1 ppm, produce distinct visual color changes, demonstrating the relationship between concentration and observable properties.
What is the approximate temporal equivalent of one part per trillion (ppt)?
Answer: Thirty seconds out of a million years
The temporal analogy for one part per trillion (10<sup>-12</sup>) is approximately thirty seconds within a span of one million years, illustrating its extreme smallness.
How is a strain of 2 cm/m represented using parts-per notation?
Answer: 2 %
A strain expressed as 2 cm/m is equivalent to 2 parts per hundred, which is conventionally represented using the percent symbol (%) or as 2%.
What does the accuracy specification '±(1 mm + 1 ppm)' for a laser rangefinder indicate?
Answer: A combination of a fixed error (1 mm) and a distance-proportional error (1 ppm).
This specification denotes a measurement uncertainty composed of a fixed error of ±1 mm and a variable error proportional to the measured distance, equal to ±1 ppm. The total error is thus a function of both the fixed offset and the measured distance.
What is the temporal equivalent of one part per billion (ppb)?
Answer: 3 seconds in a century
The temporal analogy for one part per billion (10<sup>-9</sup>) is approximately three seconds within a century, illustrating its extremely small magnitude.
What is the temporal equivalent of one part per quadrillion (ppq)?
Answer: Approximately 2.5 minutes over the age of the Earth.
The temporal analogy for one part per quadrillion (10<sup>-15</sup>) is approximately two and a half minutes within the entire age of the Earth (circa 4.5 billion years), emphasizing its infinitesimal scale.
What does the image caption describing Fluorescein solutions illustrate?
Answer: The effect of concentration on the color of Fluorescein solutions.
The caption accompanying the Fluorescein solutions describes how varying concentrations, from 10,000 ppm down to 1 ppm, produce distinct visual color changes, demonstrating the relationship between concentration and observable properties.