Nines are an informal,

logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number to the base is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 ...

ic notation for proportions very near to one, or equivalently percentages very near 100%. Their common uses include grading the purity of materials. Put simply, "nines" are the number of consecutive nines in a

percentage In mathematics, a percentage (from la, per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also use ...

such as 99% (two nines) or a decimal fraction such as 0.999 (three nines). The number of nines of a proportion is

\mathrm = -\log_(1-x)

However, there are different conventions for stating a non-

integer An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the languag ...

number of nines. 99.5% could be expressed as "two nines five" or 2.3 nines, as outlined below. A completely pure material ( = 1) would have an infinite number of nines.

Precious metals

The exact purity of very fine precious metals such as

platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...

gold Gold is a chemical element with the symbol Au (from la, aurum) and atomic number 79. This makes it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile ...

and

silver Silver is a chemical element with the symbol Ag (from the Latin ', derived from the Proto-Indo-European ''h₂erǵ'': "shiny" or "white") and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical ...

can be of great interest. Based on the system of

millesimal fineness The fineness of a precious metal object (coin, bar, jewelry, etc.) represents the weight of ''fine metal'' therein, in proportion to the total weight which includes alloying base metals and any impurities. Alloy metals are added to increase hardne ...

, 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 way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...

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.

Other Uses

The nines scale is also sometimes used in describing the purity of bottled gases. The purity of gas is an indication of the amount of other gases it contains. A high purity refers to a low amount of other gases. Gases of higher purity are 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 giving the "number of nines" in the

or decimal fraction. For gasses, the number of nines is usually written after the letter N, rather than before it. An N2.0 gas is 99% pure, and 1% (by volume) impurities. An N6.0 gas is 99.9999% (six nines) pure, with 1 part per million (1 ppm) impurities. Intermediate values are formed using the

common logarithm In mathematics, the common logarithm is the logarithm with base 10. It is also known as the decadic logarithm and as the decimal logarithm, named after its base, or Briggsian logarithm, after Henry Briggs, an English mathematician who pioneered ...

. For example, a gas which is 99.97% pure would be described as N3.5, since log₁₀(0.03%) = −3.523. Nines are used in a similar manner to describe computer system availability.

Precious metals

Other Uses

References

See also