Play Video
1
Chemistry Tutorial 10.2b:  Concentration - Parts Per Million And Percent By Mass Volume
Chemistry Tutorial 10.2b: Concentration - Parts Per Million And Percent By Mass Volume
::2009/10/05::
Play Video
2
Calculating Part Per Million (ppm)
Calculating Part Per Million (ppm)
::2012/08/25::
Play Video
3
Concentration of Solutions: PPM and PPB Parts Per M/B
Concentration of Solutions: PPM and PPB Parts Per M/B
::2010/02/18::
Play Video
4
Parts per Million Example
Parts per Million Example
::2012/11/08::
Play Video
5
Parts Per Billion Trailer (2014)
Parts Per Billion Trailer (2014)
::2014/08/25::
Play Video
6
Parts Per Million (ppm) in NMR Spectroscopy Example
Parts Per Million (ppm) in NMR Spectroscopy Example
::2014/05/09::
Play Video
7
Powers of Ten™ (1977)
Powers of Ten™ (1977)
::2010/08/26::
Play Video
8
Одна миллиардная доля (Parts Per Billion) 2014 Фантастическая Драма США бюджет $1 300 000
Одна миллиардная доля (Parts Per Billion) 2014 Фантастическая Драма США бюджет $1 300 000
::2014/04/01::
Play Video
9
Musescore in 10 Easy Steps: Part 9 Drum Parts
Musescore in 10 Easy Steps: Part 9 Drum Parts
::2010/12/15::
Play Video
10
Symphony Pro - Music Notation on the iPad
Symphony Pro - Music Notation on the iPad
::2011/09/30::
Play Video
11
Partes por Bilhão (Parts Per Billion, 2014) - Trailer HD Oficial
Partes por Bilhão (Parts Per Billion, 2014) - Trailer HD Oficial
::2014/05/19::
Play Video
12
Basic Sibelius 6 Percussion Notation
Basic Sibelius 6 Percussion Notation
::2012/11/27::
Play Video
13
Cakewalk Sonar Working with Notation 1 of 2
Cakewalk Sonar Working with Notation 1 of 2
::2013/11/14::
Play Video
14
Beethoven, Symphony 5
Beethoven, Symphony 5
::2009/07/15::
Play Video
15
Lambda Days -  Jamie Allen - FP Performance and Scala: Beyond Big O Notation
Lambda Days - Jamie Allen - FP Performance and Scala: Beyond Big O Notation
::2014/04/04::
Play Video
16
Sibelius tutorial: The 1 Minute Drum Part
Sibelius tutorial: The 1 Minute Drum Part
::2009/10/07::
Play Video
17
Guitar Pro 6 tutorial - Drum notation
Guitar Pro 6 tutorial - Drum notation
::2011/01/12::
Play Video
18
TREMOLO: Finale 2010 Music Notation Software Tutorial #1
TREMOLO: Finale 2010 Music Notation Software Tutorial #1
::2010/10/27::
Play Video
19
J. S. Bach: Air (Classical guitar)
J. S. Bach: Air (Classical guitar)
::2007/02/08::
Play Video
20
Paramore - Ignorance [Drums Notation Score Sheet] (By OXZ)
Paramore - Ignorance [Drums Notation Score Sheet] (By OXZ)
::2010/04/20::
Play Video
21
Grade 7 Math - CST Released Question #1 (Scientific Notation)
Grade 7 Math - CST Released Question #1 (Scientific Notation)
::2014/04/02::
Play Video
22
Sonar Producer Edition 8, (Staff View) Notation
Sonar Producer Edition 8, (Staff View) Notation
::2010/04/15::
Play Video
23
Pachelbel, Canon in D (1 of 3), performed by Voices of Music
Pachelbel, Canon in D (1 of 3), performed by Voices of Music
::2009/10/28::
Play Video
24
PPM or parts per million
PPM or parts per million
::2013/09/13::
Play Video
25
Orchestration Weekly Tip: Harp Pedal Shortcuts
Orchestration Weekly Tip: Harp Pedal Shortcuts
::2013/01/12::
Play Video
26
Gabrieli, Canzon per sonare no. 2, brass choir, animated score
Gabrieli, Canzon per sonare no. 2, brass choir, animated score
::2010/05/16::
Play Video
27
Scientific Notation (Part 1)
Scientific Notation (Part 1)
::2010/12/16::
Play Video
28
Gabrieli, Canzon per sonare no. 2, brass choir, bar-graph score
Gabrieli, Canzon per sonare no. 2, brass choir, bar-graph score
::2010/05/17::
Play Video
29
Physics Vectors Converting Polar notation to Rectangular Notation
Physics Vectors Converting Polar notation to Rectangular Notation
::2013/10/23::
Play Video
30
scientific notation
scientific notation
::2011/04/07::
Play Video
31
Mind Boggling but Simple Beginner
Mind Boggling but Simple Beginner's Polyrhythm, 3:2 as 2/6 : 3/4 (Ferneyhough's notation)
::2012/10/23::
Play Video
32
John Cage: Fontana Mix (1958)
John Cage: Fontana Mix (1958)
::2011/03/20::
Play Video
33
1.1 Introduction and scientific notation
1.1 Introduction and scientific notation
::2014/07/07::
Play Video
34
Parts Per Billion 2014
Parts Per Billion 2014
::2014/10/03::
Play Video
35
Convert between scientific notation and standard notation
Convert between scientific notation and standard notation
::2011/08/17::
Play Video
36
1 3 1 Rounding and Scientific Notation mpeg2video
1 3 1 Rounding and Scientific Notation mpeg2video
::2012/08/04::
Play Video
37
La Contessa - Due Canone Per Tre Violini O Cornetti (Regensburg c.1602) - Mirror
La Contessa - Due Canone Per Tre Violini O Cornetti (Regensburg c.1602) - Mirror
::2012/07/22::
Play Video
38
Converting ppm to % explanation, for mining
Converting ppm to % explanation, for mining
::2012/05/25::
Play Video
39
Slow Swing Blues in G for Drums
Slow Swing Blues in G for Drums
::2014/04/18::
Play Video
40
Finale 2006: 16 Page Layout - Systems per page
Finale 2006: 16 Page Layout - Systems per page
::2009/04/16::
Play Video
41
How to Elaborate Use Case with UML Sequence Diagram
How to Elaborate Use Case with UML Sequence Diagram
::2013/10/02::
Play Video
42
Careless Whisper (Saxophone Sheet Music)
Careless Whisper (Saxophone Sheet Music)
::2013/11/09::
Play Video
43
17 lbs of CO2 produced per Gallon of Gasoline
17 lbs of CO2 produced per Gallon of Gasoline
::2009/04/05::
Play Video
44
Frozen - Let It Go - Piano Vocal Sheet music
Frozen - Let It Go - Piano Vocal Sheet music
::2013/12/24::
Play Video
45
Tutorial 3 - Imparare Musescore
Tutorial 3 - Imparare Musescore
::2011/11/19::
Play Video
46
How to solve a 4x4x4 Rubik
How to solve a 4x4x4 Rubik's Cube (1/3)
::2007/12/12::
Play Video
47
Let It Go Piano Tutorial with Sheet Music - Disney
Let It Go Piano Tutorial with Sheet Music - Disney's Frozen Soundtrack
::2013/12/11::
Play Video
48
Jarrod Radnich - Virtuosic Piano Solo - Pirates of the Caribbean
Jarrod Radnich - Virtuosic Piano Solo - Pirates of the Caribbean
::2013/01/06::
Play Video
49
Cu6L3 Integration by parts antidifferentiation
Cu6L3 Integration by parts antidifferentiation
::2014/02/25::
Play Video
50
Valence Electrons and the Periodic Table
Valence Electrons and the Periodic Table
::2012/12/19::
NEXT >>
RESULTS [51 .. 101]
From Wikipedia, the free encyclopedia
  (Redirected from Parts per trillion)
Jump to: navigation, search
For the film, see Parts per Billion.
One part per trillion (1 ppt) is a proportion equivalent to a drop of water diluted into 20 Olympic-size swimming pools.

In science and engineering, the parts-per notation is a set of pseudo units to describe 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 ppm (parts-per-million, 10–6), ppb (parts-per-billion, 10–9), ppt (parts-per-trillion, 10–12) and ppq (parts-per-quadrillion, 10-15).

Overview[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 unit “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 gram of water with 1 mL of water. Consequently, ppm corresponds to 1 mg/L and 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.”[1]

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 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”).[2]

Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the coefficient of thermal expansion of a certain brass alloy, α = 18.7 ppm/°C, may be expressed as 18.7 (µm/m)/°C, or as 18.7 (µin/in)/°C; the numeric value representing a relative proportion does not change with the adoption of a different unit of measure.[3] Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Qp = 125 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 (NMR) spectroscopy[edit]

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]

  • One part per hundred is generally represented by the percent (%) symbol and denotes one part per 100 parts, one part in 102, and a value of 1 × 10−2. This is equivalent to approximately one drop of water diluted into 5 milliliters (one spoonful) or about fifteen minutes out of one day.

  • 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 millage () symbol. Note however, that specific disciplines such oceanography, as well as educational exercises, do use the "ppt" abbreviation. "One part per thousand" denotes one part per 1000 parts, one part in 103, and a value of 1 × 10−3. This is equivalent to one drop of water diluted into 50 milliliters (ten spoon-fulls) or about one and a half minutes out of one day.
  • One part per ten thousand is denoted by the permyriad () symbol. In contrast, in finance, the basis point is a quantity with dimensions of (time−1) and is typically used to denote changes in or differences between percentage interest rates. 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. Although rarely used in science (ppm is typically used instead), one permyriad has an unambiguous value of one part per 10,000 parts, one part in 104, and a value of 1 × 10−4. This is equivalent to one drop of water diluted into half a liter or about nine seconds out of one day.

  • One part per million (ppm) denotes one part per 1,000,000 parts, one part in 106, 1/1,000,000 * 100% = 0.0001% (or 1% = 10,000 ppm), and a value of 1 × 10−6. This is equivalent to one drop of water diluted into 50 liters (roughly the fuel tank capacity of a compact car) or about 32 seconds out of a year.

  • One part per billion (ppb) denotes one part per 1,000,000,000 parts, one part in 109, 1/1,000,000,000 * 100% = 0.0000001% (or 1% = 10,000,000 ppb) and a value of 1 × 10−9. This is equivalent to one drop of water diluted into 250 chemical drums (50 m3), or about three seconds out of a century.

  • One part per trillion (ppt) denotes one part per 1,000,000,000,000 parts, one part in 1012, and a value of 1 × 10−12. This is equivalent to one drop of water diluted into 20 Olympic-size swimming pools (50,000 m3), or about three seconds out of every hundred thousand years.

  • One part per quadrillion (ppq) denotes one part per 1,000,000,000,000,000 parts, one part in 1015, and a value of 1 × 10−15. This is equivalent to 1 drop of water diluted into a cube of water measuring approximately 368 meters on a side (fifty million cubic meters, which is a cube about as tall as the Empire State Building's 102 stories), or 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.[4]

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).[2] Note that although “percent” (%) is not formally part of the SI, both the BIPM and the 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.[2][5] According to IUPAP, “a continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt.”[6]. 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 the following:

Long and short scales[edit]

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. In the English language, named numbers have a consistent meaning only up to “million”. Starting with “billion”, there are two numbering conventions: the “long” and “short” scales, and “billion” can mean either 1012 or 109. 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.”[7]

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 guessed from the context.

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 unit as kg/kg, mol/mol or m3/m3 (even though they are all dimensionless).[8] 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. For volume fraction, the suffix "V" or "v" is sometimes appended to the parts-per notation (e.g., ppmV, ppbv, pptv).[9][10] Unfortunately, ppbv and pptv are also often used for mole fractions (which is identical to volume fraction only for ideal gases).

The usage is generally quite fixed inside most specific branches of science, leading some researchers to draw the conclusion that their own usage (mass/mass, mol/mol, volume/volume, or others) is the only correct one. This, in turn, leads them to not specify their 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. Many academic papers of otherwise excellent level fail to specify their usage of the parts-per notation.

SI-compliant expressions[edit]

SI-compliant units that can be used as alternatives are shown in the chart below. Expressions that the BIPM does not explicitly recognize as being suitable for denoting dimensionless quantities with the SI are shown in underlined green text.

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 min. 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 all dimensionless quantities; that is, the units of measurement factor out in expressions like “1 nm/m” (1 nm/m = 1 nano = 1 × 10−9) so the quotients are pure-number coefficients with values less than 1.

Uno[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.[6] This symbol is not to be confused with the always-italicized symbol for the variable 'uncertainty' (symbol: U). This unit name uno and its symbol could be used in combination with the SI prefixes to express the values of dimensionless quantities which are much less—or even greater—than one.[12]

Common parts-per notations in terms of the uno are given in the table below.

IUPAP's "uno" proposal
Coefficient Parts-per example Uno equiv. Symbol form Value of quantity
10−2 2% 2 centiuno 2 cU 2 × 10−2
10−3 2 ‰ 2 milliuno 2 mU 2 × 10−3
10−6 2 ppm 2 microuno 2 µU 2 × 10−6
10−9 2 ppb 2 nanouno 2 nU 2 × 10−9
10−12 2 ppt 2 picouno 2 pU 2 × 10−12

In 2004, a report to the International Committee for Weights and Measures (known also by its French-language initials CIPM) stated that response to the proposal of the uno "had been almost entirely negative" and the principal proponent "recommended dropping the idea".[13] To date, the uno has not been adopted by any standards organization and it appears unlikely it will ever become an officially sanctioned way to express low-value (high-ratio) dimensionless quantities. The proposal was instructive, however, as to the perceived shortcomings of the current options for denoting dimensionless quantities.

Improper applications[edit]

Parts-per notation may properly be used only to express true dimensionless quantities; that is, the units of measurement must cancel in expressions like "1 mg/kg" so that the quotients are pure numbers with values less than 1. Mixed-unit quantities such as "a radon concentration of 15 pCi/L" are not dimensionless quantities and may not be expressed using any form of parts-per notation, such as "15 ppt". Other examples of measures that are not dimensionless quantities are as follows:

Note however, that it is not uncommon to express aqueous concentrations—particularly in drinking-water reports intended for the general public—using parts-per notation (2.1 ppm, 0.8 ppb, etc.) and further, for those reports to state that the notations denote milligrams per liter or micrograms per liter. Although "2.1 mg/L" is not a dimensionless quantity, it is assumed in scientific circles that "2.1 mg/kg" (2.1 ppm) is the true measure because one liter of water has a mass of about one kilogram, The goal in all technical writing (including drinking-water reports for the general public) is to clearly communicate to the intended audience with minimal confusion. Drinking water is intuitively a volumetric quantity in the public’s mind so measures of contamination expressed on a per-liter basis are considered to be easier to grasp. Still, it is technically possible, for example, to "dissolve" more than one liter of a very hydrophilic chemical in 1 liter of water; parts-per notation would be confusing when describing its solubility in water (greater than a million parts per million), so one would simply state the volume (or mass) that will dissolve into a liter, instead.

When reporting air-borne rather than water-borne densities, a slightly different convention is used since air is approximately 1000 times less dense than water. In water, 1 µg/m3 is roughly equivalent to parts-per-trillion whereas in air, it is roughly equivalent to parts-per-billion. Note also, that in the case of air, this convention is much less accurate. Whereas one liter of water is almost exactly 1 kg, one cubic meter of air is often taken as 1.143 kg—much less accurate, but still close enough for many practical uses.[citation needed]

See also[edit]

References[edit]

  1. ^ 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. 
  2. ^ a b c BIPM: 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one 
  3. ^ 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 59 that of a Celsius-sized interval, the value is typically expressed as 10.4 (µin/in)/°F rather than 18.7 (µin/in)/°C. 
  4. ^ 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. The ability to chemically detect contaminants at this level is truly an impressive feat; 0.013 ppq is equivalent to the thickness of a sheet of paper versus a journey of 146,000 trips around the world. 
  5. ^ Quantities and units - Part 0: General principles, ISO 31-0:1992. 
  6. ^ a b Report to the 1999 IUPAP General Assembly: Report on recent Committee activities on behalf of IUPAP by Brian W Petley September 1998 
  7. ^ NIST: Rules and Style Conventions for Expressing Values of Quantities: 7.10.3 ppm, ppb, and ppt 
  8. ^ Schwartz and Warneck (1995). "Units for use in atmospheric chemistry". Pure Appl. Chem 67: 1377–1406. Retrieved March 9, 2011. 
  9. ^ "EPA On-line Tools for Site Assessment Calculation: Indoor Air Unit Conversion". Environmental Protection Agency. 
  10. ^ Milton R. Beychok (2005). "Air Dispersion Modeling Conversions and Formulas". Fundamentals of Stack Gas Dispersion (4th ed.). Milton R. Beychok. ISBN 0964458802. 
  11. ^ Compliance with the SI regarding the percent symbol (%) is limited in this chart. According to the BIPM’s SI brochure: Subsection 5.3.3, Formatting the value of a quantity, a space is always used to separate the unit symbol from the numeric value. Notable exceptions are the unit symbols for degree, minute, and second for plane angle, °, ′, and ″ (e.g., a latitude of 47° 38′ 8.8″). However, according to 5.3.7 Stating values of dimensionless quantities, or quantities of dimension one, the exception does not apply to the “%” symbol; it states as follows: “When it [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’s Manual of Style, and is not observed here. 
  12. ^ Certain mathematical functions can produce proportional quantities with values greater than 1. 
  13. ^ Report of the 16th meeting (13–14 May 2004), by the Consultative Committee for Units, to the International Committee for Weights and Measures, of the International Bureau of Weights and Measures (1.1 MB PDF, here). 

External links[edit]

  • National Institute of Standards and Technology (NIST): Home page
  • International Bureau of Weights and Measures (BIPM): Home page
Wikipedia content is licensed under the GFDL License
Powered by YouTube
MASHPEDIA
LEGAL
  • Mashpedia © 2014