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The reference frequency depends on the instrument's magnetic field and the element being measured. It represents the difference of a measured frequency in parts per million from the reference frequency. In nuclear magnetic resonance spectroscopy (NMR), chemical shift is usually expressed in ppm. In nuclear magnetic resonance (NMR) spectroscopy Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Q p = 125 ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125 μL/L, 125 μ gal/gal, 125 cm 3/ m 3, etc. For instance, the coefficient of thermal expansion of a certain brass alloy, α = 18.7 ppm/☌, may be expressed as 18.7 ( μm/m)/☌, or as 18.7 (μ in/in)/☌ the numeric value representing a relative proportion does not change with the adoption of a different unit of length. Parts-per notations may be expressed in terms of any unit of the same measure. "2 ppb" would generally be interpreted as "two parts in a billion parts"). However, they generally take the literal "parts per" meaning of a comparative ratio (e.g. 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. In fractions like "2 nanometers per meter" (2 n m/ m = 2 nano = 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. Parts-per notations are all dimensionless quantities: in mathematical expressions, the units of measurement always cancel. 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." Parts-per notation is also employed to denote the change, stability, or uncertainty in measurements. 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/☌". Similarly, parts-per notation is used also in physics and engineering to express the value of various proportional phenomena.
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Consequently, 1 ppm corresponds to 1 mg/L and 1 ppb corresponds to 1 μg/L. Therefore, it is common to equate 1 kilogram of water with 1 L of water. When working with aqueous solutions, it is common to assume that the density of water is 1.00 g/mL. 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. Parts-per notation is often used describing dilute solutions in chemistry, for instance, the relative abundance of dissolved minerals or pollutants in water. 1.1 In nuclear magnetic resonance (NMR) spectroscopy.