<unk> -per”<unk>   is used, especially in science and engineering, to denote relative proportions in measured quantities;<unk> cularly in low-value (high-ratio) proportions at the<unk> -per-million (ppm),<unk> -per-billion (ppb), and<unk> -per-trillion (ppt) level. Since<unk> s are quantity-per-quantity measures, they are known as dimensionless quantities; that is, they are pure numbers with no associated units of measurement. In regular prose,<unk> s generally take the literal<unk> <unk> ” meaning of a comparative ratio. However, in mathematical expressions,<unk> s function as coefficients with values less than 1.<unk>  is often used in the measure of dilutions (concentrations) in chemistry; for instance, for measuring the relative abundance of dissolved minerals or pollutants in water. The expression “1 ppm” means a given property exists at a relative proportion of one<unk><unk>  million<unk>  examined, as would occur if a water-borne pollutant was present at a concentration of one-millionth of a gram<unk>  gram of sample solution.
Similarly,<unk>  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<unk>  meter of length for every degree Celsius and this would be expressed as “α = 1.2 ppm/°C.”<unk>  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 mm<unk>  km of distance; this could be expressed as “Accuracy = 1 ppm.”
The above<unk> s are all dimensionless quantities; that is, in mathematical expressions, the units of measurement always cancel in fractions like “2 nanometers<unk>  meter” (2 nm/m = 2 nano = 2 × 10–9 = 2 ppb = 2 × 0.000000001) so the quotients are pure-number coefficients with values less than 1. When<unk> s, including the<unk> cent symbol (%), are used in regular prose (as opposed to mathematical expressions), they are still pure-number dimensionless quantities, however, they generally take the literal<unk> <unk> ” meaning of a comparative ratio (e.g., “2 ppb” would generally be interpreted as “two<unk>  in a billion<unk> ”).
Note that although the International Bureau of Weights and Measures (an international standards organization known also by its French-language initials BIPM) recognizes the use of<unk> , it is not formally<unk> of the International System of Units (SI). Consequently, according to IUPAP, “a continued source of annoyance to unit purists has been the continued use of<unk> cent, ppm, ppb, and ppt.” Also, 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. Nevertheless,<unk> ,<unk> cularly the expression “ppm”, remains widely used in technical disciplines because of its convenience in denoting dimensionless quantities. See Alternatives to<unk> , below.
Parts-per notation
Kick chart
Octane rating
Feldenkrais method
Cartesian coordinate system
Extraction ratio
Electromagnetic spectrum
Big Mac Index