**Group 1: Applications of Parts-per Notation**

– Parts-per notation used in chemistry for dilute solutions

– 1ppm corresponds to 1mg/L in water solutions

– Parts-per notation in physics/engineering for proportional phenomena

– Dimensionless quantities in parts-per notation

– Parts-per notations expressed in various units

– Usage of parts-per notations in different fields

**Group 2: Parts-per Expressions**

– Percent, permille, per10,000, per100,000, permillion, perbillion

– Representation of 1%, 1‰, 1‱, 1 pcm, and 1 ppm

– Equivalents of parts per hundred, thousand, ten thousand, hundred thousand, million, billion

– Specific values and meanings of each parts-per expression

**Group 3: Criticism of Parts-per Notation**

– Parts-per notation not formally part of the International System of Units (SI)

– Use of percent symbol recognized in mathematical expressions

– Annoyance among unit purists regarding parts-per notation

– Problems associated with parts-per notation outlined

**Group 4: Long and Short Scales Impact**

– BIPM suggests avoiding ppb and ppt due to differing values in countries

– NIST’s position on language-dependent terms with SI

– Importance of clarity in using parts-per notation

– Recommendations for standardization in parts-per expressions

**Group 5: Conversion and Specific Notations**

– Mass fraction, mole fraction, volume fraction

– Better to specify units as kg/kg, mol/mol, or m

– Conversion factor between mass fraction of 1ppb and mole fraction of 1ppb is about 4.7 for CFC-11 in air

– Suffix V or v sometimes added for volume fraction (e.g. ppmV, ppbv, pptv)

– SI-compliant expressions

– Notations for dimensionless quantities provided in scientific notation

In science and engineering, the **parts-per notation** is a set of pseudo-units to describe 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}) and **parts-per-quadrillion** (**ppq**, 10^{−15}). This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.