Parts-per notation

"Parts-per" notation is used in science and engineering, to denote proportionalities in measured quantities such as 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.

Parts per million (ppm)

In the United States and most other countries, 1 million is 1×10⁶ and "one part per million parts" (1 ppm) has a numerical value of 1×10^-6.

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 ppm means a given property exists at a 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 proportions. For example, a metal might expand 1.2 micrometre per metre of length for every degree Celsius and this would be expressed as a coefficient of thermal expansion of 1.2 ppm/°C. As another example, the accuracy of land-survey distance measurements when using a laser rangefinder might be 1 millimetre per kilometre of distance and this could be expressed as an accuracy of 1 ppm.

Parts per billion (ppb)

In the United States, 1 billion is 1×10⁹ and "one part per billion parts" (1 ppb) has a numerical value of 1×10^-9. This terminology should be used with great caution because:

• In France and frequently in continental Europe, 1×10⁹ is 1 milliard
• In the United Kingdom and in other nations using British English, 1×10⁹ is 1 thousand million and 1 billion is 1×10¹²

Parts per trillion (ppt)

In the United States, 1 trillion is 1×10¹² and "one part per trillion parts" (1 ppt) has a numerical value of 1×10^-12. This terminology should also be used with great caution because:

• In the United Kingdom and other nations using British English, France and continental Europe, 1×10¹² is 1 billion and 1 trillion is 1×10¹⁸

• Concentrations are sometimes expressed as ppt meaning parts per thousand which conflicts with ppt meaning parts per trillion.

Summary of large number names

Names Of Large Numbers

Value	United States	United Kingdom	Europe	SI prefix
106	million	million	million	mega
109	billion	thousand million	milliard	giga
1012	trillion	billion	billion	tera
1015	quadrillion	thousand billion	billiard	peta
1018	quintillion	trillion	trillion	exa

It should be noted that in the United States, the natural gas and petroleum refining industries commonly use the letter M to denote one thousand (10³ ) and the letters MM to denote one million (10⁶ ).

Differentiation between volume and weight proportionalities

The notation ppmv is often used to designate parts per million parts by volume and ppmw is often used to designate parts per million by weight.

Similarly, ppbv, ppbw, pptv and pptw have the same connotations.

Summary

The parts-per notation is not formally part of the International System of Units (SI).

The International Bureau of Weights and Measures (an international standards organization known also by its French-language initials BIPM) recognizes the use of parts-per notation. However, the BIPM suggests avoiding the use of ppb and ppt to avoid misunderstandings.

Perhaps the best practice is to use the scientific notations 1×10^-6, 1×10^-9 and 1×10^-12 to avoid misunderstandings.