Editing Parts-per notation (section)

== 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&nbsp;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 solution]]s, it is common to assume that the density of water is 1.00&nbsp;g/mL. Therefore, it is common to equate 1&nbsp;kilogram of water with 1&nbsp;L of water. Consequently, 1&nbsp;ppm corresponds to 1&nbsp;mg/L and 1&nbsp;ppb corresponds to 1&nbsp;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&nbsp;[[micrometre|micrometers]] per [[metre|meter]] of length for every [[Celsius|degree Celsius]] and this would be expressed as {{nobr|"[[coefficient of thermal expansion|{{mvar|α}}]] {{=}} 1.2 ppm/°C".}} Parts-per notation is also employed to denote the change, stability, or [[standard deviation|uncertainty]] in measurements. For instance, the accuracy of land-survey distance measurements when using a [[laser rangefinder]] might be 1&nbsp;millimeter per kilometer of distance; this could be expressed as "[[Accuracy and precision|Accuracy]]&nbsp;=&nbsp;1&nbsp;ppm."{{efn|
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 {{nobr|±(1 mm + 1 ppm)".}} Consequently, a distance measurement of only a few meters would still have an accuracy of ±1&nbsp;mm in this example.
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Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. In fractions like "2&nbsp;nanometers per meter" {{nobr|(2 n <s>m</s> / <s>m</s> {{=}} 2 nano {{=}} 2×{{10^|−9}} {{=}} 2 ppb {{=}} 2 × {{val|0.000,000,001}}),}} so the [[quotient]]s are pure-number [[coefficient]]s with positive values less than or equal to&nbsp;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&nbsp;ppb" would generally be interpreted as "two parts in a billion parts").<ref name=BIPM>{{cite web |title=Stating values of dimensionless quantities, or quantities of dimension one |at=§&nbsp;5.3.7 |website=BIPM |url=http://www.bipm.org/en/publications/si-brochure/section5-3-7.html}}</ref>

Parts-per notations may be expressed in terms of any unit of the same measure. For instance, the [[coefficient of thermal expansion|expansion coefficient]] of some [[brass]] alloy, {{nobr|[[coefficient of thermal expansion|{{mvar|α}}]] {{=}} 18.7 ppm/°C,}} may be expressed as 18.7&nbsp;([[micrometre|μm]]/[[meter|m]])/°C, or as 18.7&nbsp;(μ [[inch|in]]/[[inch|in]])/°C; the numeric value representing a relative proportion does not change with the adoption of a different unit of length.{{efn|
In the particular case of coefficient of thermal expansion, the change to inches (one of the [[United States customary units|U.S. customary units]]) is typically also accompanied by a change to [[Fahrenheit|degrees Fahrenheit]]. Since a Fahrenheit-sized interval of temperature is only {{sfrac| 5 |9}} that of a Celsius-sized interval, the value is typically expressed as {{nobr|10.4 (μ [[inch|in]]/[[inch|in]])/°F}} rather than {{nobr|18.7 (μ [[inch|in]]/[[inch|in]])/°C.}}
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Similarly, a [[metering pump]] that injects a trace chemical into the main process line at the proportional flow rate {{nobr|[[volumetric flow rate|{{mvar|Q}}]]{{sub|p}} {{=}} 12 ppm,}} is doing so at a rate that may be expressed in a variety of volumetric units, including {{nobr|125 μ[[litre|L]]/[[litre|L]],}} {{nobr|125 μ [[Gallon|gal]] / [[Gallon|gal]],}} 125&nbsp;cm<sup>3</sup>/[[cubic metre|m<sup>3</sup>]], 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 ([[Hertz (unit)|Hz]]/MHz). Parts-per notation gives a dimensionless quantity that does not depend on the instrument's field strength.