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# 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.

## Contents

## 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.

## 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}.

## 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*.

## 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.

## 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.^{[1]} However, the BIPM suggests avoiding the use of ppb and ppt to avoid misunderstandings.

The International Organization for Standardization technical standard ISO 80000-1:2009, clause 6.5.5, advocates the use of powers of ten per cubic meter or per kilogram rather than any of the parts-per notation (i.e., ppm, ppb or ppt). Complying with ISO standard would avoid any of the problems associated with the various definitions of billion and trillion in countries other than the United States.

The United States' National Institute of Standards and Technology includes this statement in their *NIST Guide to the SI* :^{[2]}

Because the names of numbers 109 and larger are not uniform worldwide, it is best that they be avoided entirely (in many countries, 1 billion = 1 × 1012, not 1 × 109 as in the United States); the preferred way of expressing large numbers is to use powers of 10. This ambiguity in the names of numbers is one of the reasons why the use of ppm, ppb, ppt, and the like is deprecated.

Despite the above stated positions of the International Organization for Standardization and the United States' National Institute of Standards and Technology, the technical literature continues to use the parts-per notation quite often. Also, in some cases, the use of the parts-per notation is required by law.

## References

- ↑ 5.3.7
*Stating values of dimensionless quantities, or quantities of dimension one*from the website of the BIPM - ↑ NIST Guide to the SI — Rules and Style Conventions for Expressing Values of Quantities, Scroll down to Section 7.10.3.