In science and engineering, parts-per notation is a set of pseudo-units to describe the small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are
parts-per-million – ppm, 10−6 parts-per-billion – ppb, 10−9 parts-per-trillion – ppt, 10−12 parts-per-quadrillion – ppq, 10−15 This notation is not part of the International System of Units (the SI system) and its meaning is ambiguous. In chemistry, ambiguity arises because parts-per notation is able to be used to refer to a mole fraction and a mass fraction, which are unequal depending on the molar mass of the substance.
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 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." 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 × 0.000000001), 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"). 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. Similarly, a metering pump that injects a trace chemical into the main process line at the proportional flow rate Qp = 12 ppm, is doing so at a rate that may be expressed in a variety of volumetric units, including 125 μL/L, 125 μgal/gal, 125 cm3/m3, 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
One part per hundred is generally represented by the percent sign (%) and denotes one part per 100 (102) 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 (103) 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 (104) 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). One part per hundred thousand, per cent mille (pcm) or milli-percent denotes one part per 100,000 (105) 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 (106) 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 (109) 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 (1012) parts, and a value of 10−12. This is equivalent to about thirty seconds out of every million years.
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