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( Parts per million)
"Parts-per" notation is used, especially in science and engineering, to denote relative proportions in measured quantities; particularly in low-value (high-ratio) proportions at the parts-per-million (ppm), parts-per-billion (ppb), and parts-per-trillion (ppt) level. Since parts-per notations 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, parts-per notations generally take the literal "parts per" meaning of a comparative ratio. However, in mathematical expressions, parts-per notations function as coefficients with values less than&_160;1. Parts-per notation 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&_160;ppm" means a given property exists at a relative proportion of one part per million parts examined, as would occur if a water-borne pollutant was present at a concentration of one-millionth of a gram per gram of sample solution. 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 "a&_160;=&_160;1.2&_160;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&_160;millimeter per kilometer of distance; this could be expressed as "Accuracy&_160;=&_160;1&_160;ppm."[1] The above parts-per notations are all dimensionless quantities; that is, in mathematical expressions, the units of measurement always cancel in fractions like "2 nanometers per meter" (2&_160;nm/m&_160;= 2&_160;nano&_160;= 2&_160;×&_160;10–9&_160;= 2&_160;ppb&_160;= 2&_160;×&_160;0.000000001) so the quotients are pure-number coefficients with values less than&_160;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&_160;ppb" would generally be interpreted as "two parts in a billion parts").[2]
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