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sed to refer to a mole fraction and a mass fraction which are unequal depending on the molar mass of the substance applications 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 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 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 a 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 10 9 2 ppb 2 0 000 000 001 so 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 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 1 parts per notations may be expressed in terms of any unit of the same measure for instance the expansion coefficient of some brass alloy α 18 7 ppm c may be expressed as 18 7 μm m c or as 18 7 μ in in c the numeric value representing a relative proportion does not change with the adoption of a different unit of length b similarly a metering pump that injects a trace chemical into the main process line at the proportional flow rate q p 12 ppm is doing so at a rate that may be expressed in a variety of volumetric units including 125 μ l l 125 μ gal gal 125 cm 3 m 3 etc 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 1 of of per cent per mille per myriad per cent mille pcm per million ppm per billion ppb per trillion ppt per quadrillion ppq 1 0 1 0 01 0 001 0 0001 10 7 10 10 10 13 10 1 0 1 0 01 0 001 10 6 10 9 10 12 100 10 1 0 1 0 01 0 00001 10 8 10 11 pcm 1 000 100 10 1 0 1 0 0001 10 7 10 10 ppm 10 000 1 000 100 10 1 0 001 10 6 10 9 ppb 10 7 10 6 100 000 10 000 1 000 1 0 001 10 6 ppt 10 10 10 9 10 8 10 7 10 6 1 000 1 0 001 ppq 10 13 10 12 10 11 10 10 10 9 10 6 1 000 1 visualisation of 1 1 1 1 pcm and 1 ppm as fractions of the large block larger version one part per hundred is generally represented by the percent sign and denotes one part per 100 10 2 parts and a value of 10 2 this is equivalent to about fourteen 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 permille sign 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 10 3 parts and a value of 10 3 this is equivalent to about ninety seconds out of one day one 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 one part per 10 000 10 4 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 hundred thousand per cent mille pcm or milli percent denotes one part per 100 000 10 5 parts and a value of 10 5 it is commonly used in epidemiology for mortality crime and disease prevalence rates and nuclear reactor engineering as a unit of reactivity in time measurement it is equivalent to about 5 minutes out of a year in distance measurement it is equivalent to 1 cm of error per km of distance traversed one part per million ppm denotes one part per 1 000 000 10 6 parts and a value of 10 6 it is equivalent to about 32 seconds out of a year or 1 mm of error per km of distance traversed in mining it is also equivalent to one gram per metric ton expressed as g t one part per billion ppb denotes one part per 1 000 000 000 10 9 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 10 12 parts and a value of 10 12 this is equivalent to about thirty seconds out of every million years one part per quadrillion ppq denotes one part per 1 000 000 000 000 000 10 15 parts and a value of 10 15 this is equivalent to about 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 3 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 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 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 set out below long and short scales edit main article 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 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 determined from the context 6 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 units out such as kg kg mol mol or m 3 m 3 even though they are all dimensionless 6 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 molar mass of cfc 11 mean molar mass of air 137 368 28 97 4 74 for volume fraction the suffix v or v is sometimes appended to the parts per notation e g ppmv ppbv pptv 8 to distinguish the mass fraction from volume fraction or mole fraction the letter m for mass but is ambiguous with mole fraction or w standing for weight is sometimes added to the abbreviation e g ppmw ppbw 6 expressions such as parts per million by volume and parts per million by mass are sometimes used si compliant expressions edit 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 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 9 2 10 2 a sensitivity of 2 m v 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 μ v v 2 parts per million 2 ppm 2 10 6 a sensitivity of 2 n v 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 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 5 in 2004 a report to the international committee for weights and measures cipm stated that the response to the proposal of the uno had been almost entirely negative and the principal proponent recommended dropping the idea 10 to date the uno has not been adopted by any standards organization footnotes edit 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 edit 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 edit 1 2 3 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 146 000 trips around the world quantities and units part 0 general principles iso 31 0 1992 1 2 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 1 2 3 4 schwartz s e warneck p 1995 units for use in atmospheric chemistry iupac recommendations 1995 pdf pure and applied chemistry 67 8 9 1377 1406 doi 10 1351 pac199567081377 s2cid 7029702 nist rules and style conventions for expressing values of quantities 7 10 3 ppm ppb and ppt beychok milton r 2005 air dispersion modeling conversions and formulas fundamentals of stack gas dispersion 4th ed milton r beychok isbn 0964458802 according to bipm s si brochure section 5 3 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 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 edit look up ppm ppb ppt or ppq in wiktionary the free dictionary media related to parts per notation at wikimedia commons national institute of standards and technology nist international bureau of weights and measures bipm retrieved from https en wikipedia org w index php title parts per_notation oldid 1359383611 categories analytical chemistry chemical nomenclature dimensionless numbers environmental chemistry mathematical terminology measurement metrics physical constants units of measurement hidden categories articles with short description short description is different from wikidata commons category link from wikidata this page was last edited on 14 june 2026 at 23 59 utc page was 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