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.

1 troy ounce of four nines fine gold (999.9)

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]

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

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]