Nines are an informal

logarithm In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...

ic 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 In mathematics, a percentage () is a number or ratio expressed as a fraction (mathematics), fraction of 100. It is often Denotation, denoted using the ''percent sign'' (%), although the abbreviations ''pct.'', ''pct'', and sometimes ''pc'' are ...

such as 99% (two nines) or a

decimal fraction The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (''decimal fractions'') of the ...

such as 0.999 (three nines). Their common uses include grading the purity of materialsespecially

precious metal Precious metals are rare, naturally occurring metallic chemical elements of high Value (economics), economic value. Precious metals, particularly the noble metals, are more corrosion resistant and less reactivity (chemistry), chemically reac ...

s and

industrial gas Industrial gases are the gaseous materials that are Manufacturing, manufactured for use in Industrial sector, industry. The principal gases provided are nitrogen, oxygen, carbon dioxide, argon, hydrogen, helium and acetylene, although many other ...

esor 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) or as 2.3 nines, 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. The number of nines of a proportion is:

\mathrm = -\log_(1-x)

Uses

Precious metals

The exact purity of very fine precious metals such as

platinum Platinum is a chemical element; it has Symbol (chemistry), symbol Pt and atomic number 78. It is a density, dense, malleable, ductility, ductile, highly unreactive, precious metal, precious, silverish-white transition metal. Its name origina ...

gold Gold is a chemical element; it has chemical symbol Au (from Latin ) and atomic number 79. In its pure form, it is a brightness, bright, slightly orange-yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal ...

and

silver Silver is a chemical element; it has Symbol (chemistry), symbol Ag () and atomic number 47. A soft, whitish-gray, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal. ...

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 A logarithmic scale (or log scale) is a method used to display numerical data that spans a broad range of values, especially when there are significant differences among the magnitudes of the numbers involved. Unlike a linear Scale (measurement) ...

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. 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.

Gases

The nines scale is also used in other contexts, such as describing the purity of

gases Gas is a state of matter that has neither a fixed volume nor a fixed shape and is a compressible fluid. A ''pure gas'' is made up of individual atoms (e.g. a noble gas like neon) or molecules of either a single type of atom ( elements such ...

. The purity of a gas is an indication of the ratio of it to other gases in its

mixture In chemistry, a mixture is a material made up of two or more different chemical substances which can be separated by physical method. It is an impure substance made up of 2 or more elements or compounds mechanically mixed together in any proporti ...

, 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

. 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. 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). An alternative representation uses the

common logarithm In mathematics, the common logarithm (aka "standard logarithm") is the logarithm with base 10. It is also known as the decadic logarithm, the decimal logarithm and the Briggsian logarithm. The name "Briggsian logarithm" is in honor of the British ...

: for example, a gas which is 99.97% pure would be described as N3.5, since log₁₀(0.03%) = −3.523.

System availability

Nines are used in a similar manner to describe computer system availability. In this context, a "one nine" (90%)

uptime Uptime is a Measurement, measure of system reliability, expressed as the period of system time, time a machine, typically a computer, has been continuously working and available. Uptime is the opposite of downtime. It is often used as a measure ...

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. A "five nines" (99.999%) uptime describes a system that is unavailable for at most 26 seconds per month.

References