# Parts-per notation

*20 December 2010*.

**"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.

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## [edit] Parts per million (ppm)

In the United States and most other countries, 1 million is 1×10^{6} 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.

As an item of interest, 1 percent is equivalent to 10,000 ppm.

## [edit] Parts per billion (ppb)

In the United States, 1 billion is 1×10^{9} 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 the United Kingdom and in other nations using British English, 1×10
^{9}is*1 thousand million*and 1 billion is 1×10^{12}.

## [edit] Parts per trillion (ppt)

In the United States, 1 trillion is 1×10^{12} 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, 1×10
^{12}is*1 billion*and 1 trillion is 1×10^{18}

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

## [edit] Summary of large number names

Value | United States | United Kingdom | Europe | SI prefix |
---|---|---|---|---|

10^{6} |
million | million | million | mega |

10^{9} |
billion | thousand million | milliard | giga |

10^{12} |
trillion | billion | billion | tera |

10^{15} |
quadrillion | thousand billion | billiard | peta |

10^{18} |
quintillion | trillion | trillion | exa |

In the United States, the natural gas and petroleum refining industries
commonly use the letter M to denote one thousand (10^{3 }) and the letters MM to denote one million (10^{6 }) when stating gas volumes in cubic feet.

## [edit] 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.

## [edit] 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.^{[1]} 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.

## [edit] References

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