Parts-per notation
In
Applications
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
Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. In fractions like "2 nanometers per meter" (2 n m / m = 2 nano = 2×10−9 = 2 ppb = 2 × 0.000000001), so the
Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the
In
Parts-per expressions
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 | 0.0001 |
ppm | 10,000 | 1,000 | 100 | 10 | 1 | 0.001 |
ppb | 107 | 106 | 105 | 10,000 | 1,000 | 1 |
- One part per hundred is generally represented by the percent sign (%) and denotes one part per 100 (102) parts, and a value of 10−2. This is equivalent to about fourteen minutes out of one day.
- One part per trillion"). It may also be denoted by the permillesign (‰). 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 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 distance measurement, it is equivalent to 1 cm of error per km of distance traversed.
- One part 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 age of the Earth (4.5 billion years). Although relatively uncommon in analytical chemistry, measurements at the ppq level are sometimes performed.[3]
Criticism
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
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
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
Another problem of the parts-per notation is that it may refer to
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,
SI-compliant expressions
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 !.
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 p V/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)
Because of the cumbersome nature of expressing certain dimensionless quantities per SI guidelines, the
Footnotes
- ^ This is a simplified explanation. Laser rangefinders typically have a measurement "granularity" of one to ten millimeters; thus, the complete specification for distance measurement accuracy might read as follows: "Accuracy ±(1 mm + 1 ppm)". Consequently, a distance measurement of only a few meters would still have an accuracy of ±1 mm in this example.
- ^ In the particular case of coefficient of thermal expansion, the change to inches (one of the U.S. customary units) is typically also 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 10.4 (μ in/in)/°F rather than 18.7 (μ in/in)/°C.
See also
- International Electrotechnical Commission (IEC)
- Milligram per cent
- Percentage (%) 1 part in 100
- Per mille(‰) 1 part in 1,000
- Permyriad(‱) 1 part in 10,000
- Per cent mille (pcm) 1 part in 100,000
- Per-unit system
References
- ^ a b c "Stating values of dimensionless quantities, or quantities of dimension one". BIPM. § 5.3.7.
- ^ "Basis Points (BPS)". Corporate Finance Institute.
- ^ Measurements of dioxin are routinely made at the sub-ppq level. The U.S. Environmental Protection Agency (EPA) currently sets a hard limit of 30 ppq for dioxin in drinking water but once recommended a voluntary limit of 0.013 ppq. Also, radioactive contaminants in drinking water, which are quantified by measuring their radiation, 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 world.
- ^ Quantities and units. Part 0: General principles, ISO 31-0:1992.
- ^ a b Petley, Brian W. (September 1998). "Report on Recent Committee Activities on Behalf of IUPAP to the 1999 IUPAP General Assembly". Archived from the original on 2017-08-15. Retrieved 2017-08-15.
- ^ NIST: Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt.
- S2CID 7029702.
- Environmental Protection Agency.
- ISBN 0964458802.
- ^ "Units". Introduction to green engineering. University of Virginia. 23 August 2012.
- contrary to Wikipedia's Manual of Style, and is not observed here.
- ^ Consultative Committee for Units (13–14 May 2004). "Report of the 16th meeting (13–14 May 2004) to the International Committee for Weights and Measures, of the International Bureau of Weights and Measures" (PDF). Archived from the original (PDF) on 2014-03-10.
External links
- Media related to Parts-per notation at Wikimedia Commons
- National Institute of Standards and Technology (NIST)
- International Bureau of Weights and Measures (BIPM)