Nines (notation)

Nines are an informal logarithmic notation for proportions very near to one or, equivalently, percentages very near 100%. Put simply, "nines" are the number of consecutive nines in a percentage such as 99% (two nines)^[1] or a decimal fraction such as 0.999 (three nines). Their common uses include grading the purity of materials – especially precious metals and industrial gases – or measuring the availability of a service.

Nomenclature

The nines are a count of the leftmost digits 9 that appear in a proportion. For example, 90% would be described as "one nine"; 99% as "two nines"; 99.9% as "three nines"; and so forth.

However, there are different conventions for representing inexact multiples of 9. For example, a percentage of 99.5% could be expressed as "two nines five" (2N5, or N2.5)^[2] or as 2.3 nines,^{[citation needed]} following from the logarithm definition.

A percentage of 100% would, in theory, have an infinite number of nines – though, in the context of purity of materials, 100% is virtually unachievable.^[3]

Percent	Permille	Nines
90%	900	1 nine	1N	N1.0
99%	990	2 nines	2N	N2.0
99.9%	999	3 nines	3N	N3.0
99.95%	999.5	3 nines 5	3N5	N3.5
99.97%	999.7	3.5 nines^{[citation needed]}	?	?
99.99%	999.9	4 nines	4N	N4.0
99.995%	999.95	4 nines 5	4N5	N4.5
99.999%	999.99	5 nines	5N	N5.0
99.9999%	999.999	6 nines	6N	N6.0

The number of nines of a proportion x is:^[4]

$\mathrm {nines} =-\log _{10}(1-x)$

Uses

Precious metals

The exact purity of very fine precious metals such as platinum, gold and silver can be of great interest. Based on the system of millesimal fineness, a metal is said to be one nine or one nine fine if it is 900 fine, or 90% pure. A metal that is 990 fine is then described as two nines fine and one that is 999 fine is described as three nines fine. Thus, nines are a logarithmic scale of purity for very fine precious metals. Similarly, percentages ending in a 5 have conventional names, traditionally the number of nines, then "five", so 999.5 fine (99.95% pure) is "three nines five", abbreviated 3N5.

Canada's Big Maple Leaf, a coin made of gold at 5N (99.999%) purity, stands as the purest gold coin ever minted, anywhere.^[5] The purest gold ever achieved was reportedly produced at the Perth Mint in 1957, at "almost six nines" (99.9999%) purity, as measured by the Worshipful Company of Goldsmiths of London.^[6]

Gases

The nines scale is also used in other contexts, such as describing the purity of gases. The purity of a gas is an indication of the ratio of it to other gases in its mixture, as measured by volume. Thus, a high purity refers to a low amount of other gases, or impurities. Gases of higher purity are in many contexts considered to be of better quality and are usually more expensive.

The purity of a gas is generally expressed as a grade prefixed with the letter N (rather than postfixed), indicating the "number of nines" in the percentage or decimal fraction. For example, a N2.0 gas is 99% (two nines) pure and 1% impurities by volume; a N6.0 gas is 99.9999% (six nines) pure, with 1 part per million (1 ppm or 1 vpm, volume per million) impurities.^[7]

Intermediate values indicate the digit following the last nine. For example, N4.6 estimates a purity level of 99.996% (four nines followed by a six).^[7] An alternative representation uses the common logarithm: for example, a gas which is 99.97% pure would be described as N3.5, since log₁₀(0.03%) = −3.523.^{[citation needed]}

System availability

Nines are used in a similar manner to describe computer system availability. In this context, a "one nine" (90%) uptime indicates a system that is available 90% of the time or, as is more commonly described, unavailable 10% of the time – about 72 hours per month.^[8] A "five nines" (99.999%) uptime describes a system that is unavailable for at most 26 seconds per month.^[8]

References

^ Technical Information for Congress: Report to the Subcommittee on Science, Research and Development of the Committee on Science and Astronautics. 25 April 1969. p. 123. Retrieved 19 April 2024. For example, the difference between a purity of aluminum of "four nines" and "six nines" is understandable to a scientist, but not necessarily to a politician. (These are 99.99 percent pure and 99.9999 percent pure).
^ Davis, Joseph R. (September 2004). Handbook of Thermal Spray Technology. ASM International. p. 94. ISBN 978-0-87170-795-6. Retrieved 19 April 2024. For example, good commercial-grade gases for plasma spraying are stated to be at least 99.995% ("four-nines-five" purity).
^ Bell-Young, Lucy (18 November 2020). "What Are Pure Chemicals?". ReAgent. Retrieved 19 April 2024. Therefore, in reality, it's virtually impossible to have a 100% chemically pure substance that maintains its purity for an extended period of time.
^ jtw13 (2012-06-04). "Name that function!". AstroWright. Retrieved 2024-06-09.{{cite web}}: CS1 maint: numeric names: authors list (link)
^ Waldman, Ben (31 January 2019). "The saga of Canada's stolen million-dollar coin". Maclean's. Retrieved 19 April 2024. At "five nines pure" (99.999%) the gold contained less than 10 parts per million of other elements like silver, aluminum and zirconium, one decimal place purer and hundreds of thousands of dollars more valuable than any gold coinage minted in Vienna or elsewhere, ever.
^ "The Perth Mint story and history". Perth Mint. Retrieved 19 April 2024. We achieved "arguably the purest of all gold" in 1957. Refinery Officer Leo Hickey and Senior Craftsman Alexander Osborne produced a proof 'plate' of almost six nines - 999.999 parts of gold per thousand - as measured by the Worshipful Company of Goldsmiths in London.
^ ^a ^b "Purity, Grades, and Concentration". BOC. Retrieved 22 January 2017.
^ ^a ^b "Definition of five nines". PCMag. Retrieved 19 April 2024.