Parts-per notation

Parts-per notation is often used describing dilute solutions in chemistry, for instance, the relative abundance of dissolved minerals or pollutants in water.

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".

In fractions like "2 nanometers per meter" (2 n m / m = 2 nano = 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.

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.

[1] Note that although "percent" (%) is not formally part of the SI, both the BIPM and the International Organization for Standardization (ISO) take the position that "in mathematical expressions, the internationally recognized symbol % (percent) may be used with the SI to represent the number 0.01" for dimensionless quantities.

The U.S. National Institute of Standards and Technology (NIST) takes the stringent position, stating that "the language-dependent terms [...] are not acceptable for use with the SI to express the values of quantities".

Expressions that the BIPM explicitly does not recognize as being suitable for denoting dimensionless quantities with the SI are marked with !.

Because of the cumbersome nature of expressing certain dimensionless quantities per SI guidelines, the International Union of Pure and Applied Physics (IUPAP) in 1999 proposed the adoption of the special name "uno" (symbol: U) to represent the number 1 in dimensionless quantities.

[5] In 2004, a report to the International Committee for Weights and Measures (CIPM) stated that the response to the proposal of the uno "had been almost entirely negative", and the principal proponent "recommended dropping the idea".