4 1 4 Improper Fraction

Fix of pseudo units to describe small values of miscellaneous dimensionless quantities

Fluorescein aqueous solutions, diluted from 1 to 10,000 parts-per-million in intervals of 10 fold concentration. At 1 ppm the solution is a very pale yellowish. As the concentration increases the colour becomes a more vibrant yellow, then orange, with the last 10,000 ppm a deep ruby colour.

In science and engineering science, the parts-per notation is a ready of pseudo-units to describe minor values of miscellaneous dimensionless quantities, east.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Usually used are parts-per-million (ppm, ten⁻⁶ ), parts-per-billion (ppb, 10⁻⁹ ), parts-per-trillion (ppt, ten⁻¹² ) and parts-per-quadrillion (ppq, ten⁻¹⁵ ). This notation is non part of the International System of Units (SI) system and its meaning is ambiguous.

Overview [edit]

Parts-per notation is often used describing dilute solutions in chemical science, for instance, the relative abundance of dissolved minerals or pollutants in water. The quantity "ane 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, information technology is common to assume that the density of water is 1.00 g/mL. Therefore, it is mutual to equate one kilogram of water with 1 Fifty of water. Consequently, i ppm corresponds to ane mg/L and 1 ppb corresponds to 1 μg/L.

Similarly, parts-per notation is used besides in physics and applied science to limited the value of diverse 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 = ane.2 ppm/°C". Parts-per notation is also employed to denote the change, stability, or dubiousness 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 every bit "Accuracy = 1 ppm."^[1]

Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement e'er cancel. In fractions like "ii nanometers per meter" (2 northm/m = 2 nano = 2 × 10⁻⁹ = 2 ppb = two × 0.000000 001 ), then 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 have the literal "parts per" significant of a comparative ratio (e.k. "2 ppb" would mostly be interpreted as "two parts in a billion parts").^[2]

Parts-per notations may be expressed in terms of any unit of measurement of the same measure. For example, the coefficient of thermal expansion of a certain brass alloy, α = xviii.7 ppm/°C, may be expressed as 18.7 (μm/thousand)/°C, or as eighteen.7 (μin/in)/°C; the numeric value representing a relative proportion does not change with the adoption of a unlike unit of length.^[3] Similarly, a metering pump that injects a trace chemical into the main procedure line at the proportional flow rate Q_p = 125 ppm, is doing so at a charge per unit that may be expressed in a multifariousness of volumetric units, including 125 μL/50, 125 μgal/gal, 125 cm³/m³, etc.

In nuclear magnetic resonance (NMR) spectroscopy [edit]

In nuclear magnetic resonance spectroscopy (NMR), chemic shift is usually expressed in ppm. Information technology represents the divergence 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 chemic 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]

ane of → = ⭨ of ↓	per cent (%)	per mille (‰)	per 10,000 (‱)	per 100,000 (pcm)	per one thousand thousand (ppm)	per billion (ppb)
%	i	0.1	0.01	0.001	0.0001	x⁻⁷
‰	10	1	0.1	0.01	0.001	10^−vi
‱	100	10	1	0.1	0.01	10^−five
pcm	1,000	100	10	1	0.1	0.0001
ppm	x,000	1,000	100	10	1	0.001
ppb	10^vii	ten⁶	ten^five	10,000	1,000	1

Visualisation of 1%, 1‰, 1‱, 1 pcm and 1 ppm every bit fractions of the large block (larger version)

One part per hundred is more often than not represented by the per centum sign (%) and denotes one part per 100 (x²) parts, and a value of ten⁻². This is equivalent to virtually xv minutes out of one solar day.

I office per thousand should mostly be spelled out in full and non as "ppt" (which is usually understood to stand for "parts per trillion"). It may also be denoted by the permille sign (‰). Note nonetheless, that specific disciplines such as oceanography, every bit well every bit educational exercises, do use the "ppt" abridgement. "Ane part per grand" denotes one part per 1,000 (x³) parts, and a value of 10^−three. This is equivalent to virtually ninety seconds out of one day.
I 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 1 part per 10,000 (x⁴) parts, and a value of x⁻⁴. This is equivalent to about nine seconds out of one mean solar day.
In contrast, in finance, the basis point is typically used to announce changes in or differences between percentage interest rates (although it can as well exist used in other cases where it is desirable to express quantities in hundredths of a pct). For example, a modify in an interest rate from five.15% per annum to 5.35% per annum could exist denoted every bit a modify of twenty basis points (per annum). As with involvement rates, the words "per annum" (or "per twelvemonth") are often omitted. In that case, the basis point is a quantity with a dimension of (time⁻ⁱ).^[4]
One part per hundred one thousand, per cent mille (pcm) or milli-percent denotes ane part per 100,000 (x⁵) parts, and a value of ten^−v. It is commonly used in epidemiology for mortality, crime and affliction prevalence rates, and nuclear reactor engineering as a unit of reactivity. In fourth dimension measurement it is equivalent to about 5 minutes out of a yr; in distance measurement, information technology is equivalent to 1 cm of error per km of distance traversed.

Ane function per meg (ppm) denotes one function per 1,000,000 (x⁶) parts, and a value of ten^−six. Information technology is equivalent to near 32 seconds out of a yr or 1 mm of error per km of distance traversed.

One part per billion (ppb) denotes one part per 1,000,000,000 (ten^nine) parts, and a value of x⁻⁹. This is equivalent to virtually three seconds out of a century.

One office per trillion (ppt) denotes i part per 1,000,000,000,000 (x¹²) parts, and a value of 10⁻¹². This is equivalent to about thirty seconds out of every million years.

One office per quadrillion (ppq) denotes one role per 1,000,000,000,000,000 (10¹⁵) parts, and a value of x⁻¹⁵. This is equivalent to nigh two and a one-half minutes out of the age of the Earth (iv.5 billion years). Although relatively uncommon in analytical chemistry, measurements at the ppq level are sometimes performed.^[5]

Criticism [edit]

Although the International Bureau of Weights and Measures (an international standards organisation known too by its French-language initials BIPM) recognizes the employ of parts-per notation, it is not formally office of the International System of Units (SI).^[2] Note that although "pct" (%) is not formally part of the SI, both the BIPM and the International Organization for Standardization (ISO) have the position that "in mathematical expressions, the internationally recognized symbol % (per centum) may be used with the SI to represent the number 0.01" for dimensionless quantities.^[2] ^[6] Co-ordinate to IUPAP, "a continued source of annoyance to unit purists has been the connected apply of percentage, ppm, ppb, and ppt".^[7] Although SI-compliant expressions should be used every bit an alternative, the parts-per notation remains withal widely used in technical disciplines. The main problems with the parts-per annotation are set out beneath.

Long and short scales [edit]

Because the named numbers starting with a "billion" have different values in unlike countries, the BIPM suggests avoiding the use of "ppb" and "ppt" to prevent misunderstanding. The U.Due south. National Establish of Standards and Applied science (NIST) takes the stringent position, stating that "the linguistic communication-dependent terms [...] are not acceptable for use with the SI to express the values of quantities".^[8]

Grand vs. trillion [edit]

Although "ppt" usually means "parts per trillion", information technology occasionally ways "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. book fraction [edit]

Some other problem of the parts-per note is that it may refer to mass fraction, mole fraction or volume fraction. Since it is commonly not stated which quantity is used, it is amend to write the unit as kg/kg, mol/mol or m³/mⁱⁱⁱ (even though they are all dimensionless).^[nine] The difference is quite meaning when dealing with gases, and it is very important to specify which quantity is being used. For case, the conversion factor between a mass fraction of ane ppb and a mole fraction of ane ppb is about 4.7 for the greenhouse gas CFC-11 in air. For volume fraction, the suffix "5" or "v" is sometimes appended to the parts-per notation (e.g. ppmV, ppbv, pptv).^[10] ^[11] Unfortunately, ppbv and pptv are also ofttimes used for mole fractions (which is identical to book fraction only for ideal gases).

To distinguish the mass fraction from volume fraction or mole fraction, the letter "westward" (standing for "weight") is sometimes added to the abbreviation (e.g. ppmw, ppbw).^[12]

The usage of the parts-per note is generally quite fixed inside each specific branch of science, but oftentimes 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, or others) is correct and that other usages are incorrect. This assumption sometimes leads them to non specify the details of their own usage in their publications, and others may therefore misinterpret their results. For example, electrochemists oftentimes use volume/volume, while chemical engineers may use mass/mass every bit well equally volume/volume. Many academic publications of otherwise excellent level fail to specify their usage of the parts-per note.^{[ commendation needed ]}

SI-compliant expressions [edit]

SI-compliant units that tin be used as alternatives are shown in the nautical chart beneath. Expressions that the BIPM explicitly does not recognize as beingness suitable for denoting dimensionless quantities with the SI are marked with ! .

Notations for dimensionless quantities
Measure out	SI units	Named parts-per ratio (short calibration)	Parts-per abbreviation or symbol	Value in scientific notation
A strain of...	2 cm/m	2 parts per hundred	2 %^[13]	2 × 10^−two
A sensitivity of...	2 mV/Five	two parts per g	2 ‰ !	two × x⁻³
A sensitivity of...	0.2 mV/V	2 parts per ten 1000	ii ‱ !	2 × x⁻⁴
A sensitivity of...	2 μV/V	two parts per one thousand thousand	2 ppm	2 × ten⁻⁶
A sensitivity of...	two nV/V	two parts per billion !	2 ppb !	2 × 10⁻⁹
A sensitivity of...	ii pV/V	two parts per trillion !	two ppt !	2 × x⁻¹²
A mass fraction of...	2 mg/kg	2 parts per million	two ppm	two × 10^{−half-dozen}
A mass fraction of...	2 μg/kg	two parts per billion !	two ppb !	two × ten^−nine
A mass fraction of...	2 ng/kg	2 parts per trillion !	2 ppt !	2 × 10⁻¹²
A mass fraction of...	two pg/kg	2 parts per quadrillion !	2 ppq !	2 × 10⁻¹⁵
A book fraction of...	5.ii μL/50	v.2 parts per million	5.2 ppm	v.two × 10^−six
A mole fraction of...	5.24 μmol/mol	5.24 parts per million	5.24 ppm	v.24 × 10⁻⁶
A mole fraction of...	5.24 nmol/mol	5.24 parts per billion !	5.24 ppb !	v.24 × 10⁻⁹
A mole fraction of...	five.24 pmol/mol	5.24 parts per trillion !	5.24 ppt !	v.24 × 10⁻¹²
A stability of...	ane (μA/A)/min	i role per million per minute	ane ppm/min	one × 10⁻⁶/min
A alter of...	5 nΩ/Ω	5 parts per billion !	5 ppb !	v × 10⁻⁹
An uncertainty of...	9 μg/kg	9 parts per billion !	nine ppb !	9 × 10⁻⁹
A shift of...	1 nm/grand	1 part per billion !	1 ppb !	ane × 10^−ix
A strain of...	i μm/thou	1 function per meg	one 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 alter of...	0.35 × x⁻⁹ ƒ	0.35 function per billion !	0.35 ppb !	0.35 × ten⁻⁹

Note that the notations in the "SI units" cavalcade above are all dimensionless quantities; that is, the units of measurement factor out in expressions like "1 nm/thou" (1 due northm/m = ane nano = 1 × 10⁻⁹) so the quotients are pure-number coefficients with values less than 1.

Uno (proposed dimensionless unit of measurement) [edit]

Because of the cumbersome nature of expressing sure dimensionless quantities per SI guidelines, the International Union of Pure and Practical Physics (IUPAP) in 1999 proposed the adoption of the special proper name "uno" (symbol: U) to represent the number 1 in dimensionless quantities.^[7] In 2004, a study to the International Committee for Weights and Measures (CIPM) stated that response to the proposal of the uno "had been nearly entirely negative", and the main proponent "recommended dropping the thought".^[xiv] To date, the uno has not been adopted by any standards organization, and it appears unlikely that it will ever get an officially sanctioned way to express low-value (high-ratio) dimensionless quantities.

References [edit]

^ This is a simplified caption. Light amplification by stimulated emission of radiation rangefinders typically have a measurement granularity of one to ten millimeters; thus, the complete specification for altitude measurement accurateness might read as follows: Accuracy: ±(1 mm + 1 ppm). Consequently, a distance measurement of merely a few meters would nonetheless have an accuracy of ±1 mm in this example.
^ ^a ^b ^c BIPM: 5.3.seven Stating values of dimensionless quantities, or quantities of dimension i].
^ In the detail case of coefficient of thermal expansion, the change to inches (one of the U.Due south. customary units) is typically too accompanied by a change to degrees Fahrenheit. Since a Fahrenheit-sized interval of temperature is only 5/9 that of a Celsius-sized interval, the value is typically expressed as ten.4 (μin/in)/°F rather than eighteen.7 (μin/in)/°C.
^ "What are Basis Points (BPS)?".
^ Measurements of dioxin are routinely made at the sub-ppq level. The U.S. Environmental Protection Agency (EPA) currently sets a difficult limit of 30 ppq for dioxin in drinking water merely once recommended a voluntary limit of 0.013 ppq. Also, radioactive contaminants in drinking h2o, which are quantified by measuring their radiations, are often reported in terms of ppq; 0.013 ppq is equivalent to the thickness of a sheet of paper versus a journey of 146000 trips around the earth.
^ Quantities and units. Part 0: General principles, ISO 31-0:1992.
^ ^a ^b Petley, Brian W. (September 1998). "Report on Contempo Commission Activities on Behalf of IUPAP to the 1999 IUPAP Full general Associates". Archived from the original on 2017-08-fifteen. Retrieved 2017-08-15 .
^ NIST: Rules and Mode Conventions for Expressing Values of Quantities: 7.10.iii ppm, ppb, and ppt.
^ Schwartz, Southward. E.; Warneck, P. (1995). "Units for employ in atmospheric chemistry (IUPAC Recommendations 1995)" (PDF). Pure and Applied Chemistry. 67 (eight–ix): 1377–1406. doi:10.1351/pac199567081377. S2CID 7029702.
^ "EPA On-line Tools for Site Assessment Adding: Indoor Air Unit Conversion". Environmental Protection Bureau.
^ Milton R. Beychok (2005). "Air Dispersion Modeling Conversions and Formulas". Fundamentals of Stack Gas Dispersion (4th ed.). Milton R. Beychok. ISBN0964458802.
^ "Introduction to Green Engineering science".
^ According to BIPM'south SI brochure, section 5.iii.7, "When [the percent symbol] is used, a space separates the number and the symbol %." This practice has not been well adopted with regard to the % symbol, is contrary to Wikipedia'southward Transmission of Style, and is non observed here.
^ Consultative Committee for Units (xiii–14 May 2004). "Report of the 16th meeting (xiii–fourteen May 2004) to the International Commission for Weights and Measures, of the International Bureau of Weights and Measures" (PDF). Archived from the original (PDF) on 2014-03-10.

External links [edit]

Expect up ppm , ppb , ppt , or ppq in Wiktionary, the complimentary dictionary.

Media related to Parts-per notation at Wikimedia Commons
National Institute of Standards and Technology (NIST): Habitation folio
International Bureau of Weights and Measures (BIPM): Domicile page