9 (number)


Cardinal	9 nine
Ordinal	9th ninth
Numeral system	novenary
Factorization	$3^2$
Divisors	1, 3, 9
Roman numeral	IX
Unicode representation of Roman numeral	Ⅸ, ⅸ
prefixes	ennea- (from Greek)
Binary	1001
Octal	11
Duodecimal	9
Hexadecimal	9
Arabic-Indic numeral	٩
Armenian numeral	Թ
Chinese numeral	九玖 (formal writing)
Eastern Arabic-Indic (Persian and Urdu) numeral	۹
Greek numeral	θ´
Hebrew numeral	ט (Tet)
Indian (Hindi/Devanagari) numeral	९
Japanese numeral	九玖 (formal writing)
Tamil numeral	௯
Thai numeral	๙

9 (nine) is the natural number following 8 and preceding 10.

In mathematics

Nine is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. 9 is a Motzkin number. It is the first composite lucky number.

In base 10 a number is evenly divisible by nine if and only if its digital root is 9. That is, if you multiply nine by any whole number, and repeatedly add the digits of the answer until it's just one digit, you will end up with nine:

2 × 9 = 18 (1 + 8 = 9)
3 × 9 = 27 (2 + 7 = 9)
9 × 9 = 81 (8 + 1 = 9)
234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)
578329 × 9 = 5204961 (5 + 2 + 0 + 4 + 9 + 6 + 1 = 27 (2 + 7 = 9))
482729235601 × 9 = 4344563120409 (4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45 (4 + 5 = 9))

The only other number with this property is three. In base N, the divisors of N − 1 have this property. Another consequence of 9 being 10 − 1, is that it is also a Kaprekar number.

Every prime in a Cunningham chain of the first kind with a length of 4 or greater is congruent to 9 mod 10 (the only exception being the chain 2, 5, 11, 23, 47).

Since $9 = 3^{2^1}$ , 9 is an exponential factorial.

In probability, the nine is a logarithmic measure of probability of an event, defined as the negative of the base-10 logarithm of the probability of the event's complement. For example, an event that is 99% likely to occur has an unlikelihood of 1% or 0.01, which amounts to −log₁₀ 0.01 = 2 nines of probability. Zero probability gives zero nines (−log₁₀ 1 = 0). The purity of chemicals (see Nine (purity)), the effectivity of processes, the availability of systems etc. can similarly be expressed in nines. For example, "five nines" (99.999%) availability implies a total downtime of no more than five minutes per year. This measure can be confusing, a fact which is discussed in the myth of the nines.

Six recurring nines appear in the decimal places 762 through 767 of pi. This is known as the Feynman point (see also MathWorld).

A polygon with nine sides is called an enneagon (technically) or nonagon (in common usage). A group of nine of anything is called an ennead.

In numeral systems

Base	Numeral system
2	binary	1001
3	ternary	100
4	quaternary	21
5	quinary	14
6	senary	13
7	septenary	12
8	octal	11
9	novenary	10
over 9 (decimal, hexadecimal)		9

The Arabic glyph

In the beginning, various Indians wrote 9 similar to the modern closing question mark, but dotless. The Kshtrapa, Andhra and Gupta started curving the bottom vertical line coming up with a 3-look-alike. The Nagari continued the bottom stroke to make a circle to enclose the 3-look-alike, in much the same way that the @ character encircles a lowercase a. As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, and the 3-look-alike became smaller. Soon, all that was left of the 3-look-alike was a squiggle. The Arabs simply connected that squiggle to the downward stroke at the middle and subsequent European change was purely cosmetic.

In science

Nine is the atomic number of fluorine.

Astronomy

Messier object M9 is a magnitude 9.0 globular cluster in the constellation Ophiuchus.
The New General Catalogue object NGC 9, a spiral galaxy in the constellation Pegasus

The Saros number of the solar eclipse series which began on -2568 February 6 and ended on -1252 April 4. The duration of Saros series 9 was 1316.2 years, and it contained 74 solar eclipses.
The Saros number of the lunar eclipse series which began on -2501 June 26 and ended on -1149 September 16. The duration of Saros series 9 was 1352.2 years, and it contained 76 lunar eclipses.

Nine of the bodies orbiting our Sun are considered to be planets.

In religion

The New Testament is divided into nine subsections.
Important Buddhist rituals usually involve nine monks.
The first nine days of the Hebrew month of Av are collectively known as "The Nine Days" (Tisha HaYamim), and are a period of semi-mourning leading up to Tisha B'Av, the ninth day of Av on which both Temples in Jerusalem were destroyed

In mythology

In Egyptian mythology, there are nine major gods and goddesses (see also Ennead).

Norse mythology recognized nine realms of existence. Eight of the realms were embodiments of opposites: fire and ice, heaven and hell, creation and destruction, and light and darkness. These realms all converged on the center realm. where humans lived out their lives.

The ancient Egyptians believed that a person had to earn the right to enter the afterlife. Before an individual could pass into the next realm, nine great gods known collectively as the Ennead had to judge his worthiness.

In Greek mythology, nine goddesses called the Muses were responsible for inspiring the art of musicians, artists, and writers.

In Maya mythology, nine levels existed in the underworld. Metnal, the ninth level, was a place of eternal darkness, cold, and suffering.

One of the most famous legends in Celtic mythology tells the story of nine magical hazel trees at the center of the Otherworld. They hang over the Well of Wisdom and drop their nuts into it, importing wisdom and inspiration to all who drink from the water or eat the salmon of the river.

In astrology, the ninth sign of the Zodiac is Sagittarius, identified by the Greeks as a centaur. Centaurs are magical creatures known for their skills as archers, philosophers, and predictors of the future.

As lucky or unlucky number

Nine (九 pinyin jiǔ) is considered a good number in Chinese culture because it sounds the same as the word "longlasting" (久 pinyin jiǔ). The Japanese consider 9 to be unlucky, however, because it sounds similar to the Japanese word for "pain".

Nine is strongly associated with the Chinese dragon, a symbol of magic and power. There are nine forms of the dragon, it is described in terms of nine attributes, and it has nine children.

In Thai, the word for nine, 'gao', is the same as the verb for 'to develop or progress'.

In music

In music theory a ninth is the ninth note of a musical scale or the interval between the first note and the ninth. A ninth chord is a chord with a ninth.

In classical music the curse of the ninth refers to the popular and journalistic notion that some 'mortal' significance attaches to the composition of a 'ninth' symphony, which prevents the composer from writing another. After Beethoven died leaving his Tenth Symphony unfinished, many composers were superstitious about writing Ninth Symphonies for the rest of the nineteenth century. Following the composition of his Eighth, Gustav Mahler tried to "cheat death" by disguising his next symphony as an orchestral song cycle entitled Das Lied von der Erde. Although he went on to complete a work called the Ninth Symphony (which he considered his Tenth), he died before he could complete his Tenth (or, strictly and in his mind, his Eleventh). Perhaps Antonín Dvořák was also superstitious about the number nine, because he wrote no symphonies after his New World Symphony, which is nowadays considered his Ninth, but which he thought of was his Eighth because he considered the score of his early C minor symphony lost forever. He lived for seven more years. In the twentieth century, a handful of composers, such as Dmitri Shostakovich, have written a Ninth Symphony and lived to write more.

Ralph Vaughan-Williams wrote nine complete symphonies, and the last symphony of Anton Bruckner is recognized as his ninth.

Nine is the number of Valkyries in Richard Wagner's Die Walküre.

Bands with the number nine in their name include Stroke 9, Nine Days, Nine Inch Nails and Revolution 9.

In pop music, the song "Love Potion #9" was written by Jerry Leiber and Mike Stoller (who also wrote "Riot in Cell Block No. 9"), and became a hit for The Searchers in 1965. The Beatles released a song called "Revolution 9" which appears on The White Album (more properly known as The Beatles); its principle vocal feature is a voice repeating, "Number nine...number nine...number nine..." John Lennon, the primary composer of "Revolution 9", also released a solo recording entitled "#9 Dream", leading his biographer to speculate that he had an obsession with the number.

Composer Maury Yeston adapted Fellini's 8 1/2 for Broadway as the musical Nine, which won several Tony Awards in 1982, and was successfully revived in 2003 starring Antonio Banderas.

9 is a full-length album by the heavy metal band Mercyful Fate, released in 1999. Fairport Convention also released an album with the number for a title.

In urban culture, 'nine' is a slang word for a 9mm pistol.

In sports

A batting lineup in baseball consists of nine players. In addition, 9 represents the number of innings in a game.
In chess, the maximum number of queens one side could possibly have after queening all pawns.
Nine ball is the standard professional pocket billiards variant played in the United States.
In association football a forward/striker commonly wears the number 9 shirt. For example, Alan Shearer is a famous English footballer who is known as a number 9. Another famous number 9 is Mia Hamm, who has scored more international goals than any other player of either sex.
The car number of the 1988 NASCAR Nextel Cup championship-winning team, when Bill Elliott won the title.
In rugby union the scrum-half wears the 9 shirt.
In baseball, nine represents the right fielder's position.
The retired uniform numbers of former baseball players Ted Williams and Roger Maris.
Major Harris, a football player from West Virginia University, wore number nine.
In ice hockey the number 9 is one of the most prestigious sweater numbers, having been worn by legends like Maurice Richard, Bobby Hull, and Gordie Howe. It was also worn, doubled as 99, by the great Wayne Gretzky.
Reggie Jackson wore 9 with the Oakland A's and is now retired.
Ted Williams wore 9 with the Boston Red Sox.
Ronaldo on the Brazil World Cup Team, has set the record for most goals in World Cup history. He wears number nine

In technology

ISO 9 is the ISO's standard for the transliteration of Cyrillic characters into Latin characters
In the Rich Text Format specification, 9 is the language code for the English language. All codes for regional variants of English are congruent to 9 mod 256.
On most phones, the 9 key is associated with the letters W, X, and Y (and sometimes also Z), but on the BlackBerry it is the key for M.
In Mac OS X, the F9 function key tiles all open windows and sizes them to fit together.
In computer system administration, uptime, a measure of the time a computer system has been up and running, is sometimes measured in "nines"—that is, the number of "9" digits in the percentage of time the computer is normally running. For example, "five nines" means 99.999% reliability, which translates to a total downtime of no longer than five minutes per year.

In other fields

Nine is the highest single-digit number in the decimal system.
In the NATO phonetic alphabet, the digit 9 is called "niner".
Nine is the number of musicians in a nonet.
Nine babies born into a single birth are called nonuplets, although not one baby born into a set of nonuplets has ever survived infancy.
A novena lasts for nine days.
Channel 9, an Australian free-to-air television station
Nine judges sit on the United States Supreme Court.
There are nine members of The Fellowship of the Ring in The Lord of the Rings saga, to balance and combat the nine Nazgûl, or Ringwraiths.
The ordinal adjective is nonary.
There are nine basic personality types represented on the enneagram.
In astrology, Sagittarius is the 9th astrological sign of the Zodiac.
Joel Garreau identified nine different "nations" of North America.
Nine months is approximately the gestation period for human fetuses.
A standard work day of 9 to 5 begins at 9 a.m.
Stanines are measured on a scale of 1 to 9.
Nine is a special message board on GameFAQs.
The name of the area called Kowloon in Hong Kong literally means: nine dragons.
Someone dressed "to the nines" is dressed up as much as they can be.
Number of Provinces in South Africa.
There are 9 planets in the Solar System.
Nine, as the highest single-digit number, symbolizes completeness in the Bahá'í Faith. A simple nine-pointed star is a Bahá'í symbol.
Nine Lives Cat Food got its name from the legend that a cat has nine lives.
Nine rank system
The Nine Chapters on the Mathematical Art
Nine Worthies
The Last Resort was a 1995 computer game.
Seven of Nine, fictional character from the Star Trek universe
Deep Space Nine, space station in the fictional Star Trek universe
Nine months is the average number of months per school year that most primary and secondary students are required to attend.
The Gathering has a set of nine rare cards, widely regarded as overpowered, known as the Power Nine.
In tarot, card No. 9 is "the Hermit".

Historical years

9 A.D., 9 B.C., 1909, 2009, etc.

Integers

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