# 9 number

 0 10 20 30 40 50 60 70 80 90 >> Cardinal 9 nine Ordinal 9th ninth Numeral system novenary Factorization ${\displaystyle 3^{2}}$ Divisors 1, 3, 9 prefixes ennea- (from Greek) nona- (from Latin) 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) Roman numeral IX Unicode representation of Roman numeral Ⅸ, ⅸ 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.

In base 10 a number is evenly divisible by nine if and only if the iterative sum of its digits reduces to 9. A simple way of saying this is that 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))

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.

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, 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

## The Arabic glyph

In the beginning, various Indians wrote 9 in a way that pretty much looks like our 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. (The Nagari glyph might remind some of the Baskin Robbins 31 flavors logo). 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 all the Europeans did to the glyph was purely cosmetic.

In fonts with text figures, 9 usually has a descender, for example, File:TextFigs196.png.

## 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.

According to Anton Szandor LaVey, as written on his book The Satanic Rituals, 9 is the number of Satan.

## In science

In astronomy,

Messier object M9, 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.
There are nine planets in our solar system.

## 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.

Ludwig van Beethoven, Franz Schubert, Anton Bruckner, and Ralph Vaughan Williams wrote nine symphonies. After Beethoven died leaving his Tenth Symphony unfinished, many composers were superstitious about writing Ninth Symphonies for the rest of the nineteenth century. Gustav Mahler tried to "cheat death" by writing an orchestral song cycle entitled Das Lied von der Erde instead of an instrumental Ninth Symphony. Afterwards he wrote a work called Ninth Symphony, but thought of it as his Tenth. He died with his Tenth (or, strictly and in his mind, his Eleventh) unfinished. 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.

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 and Nine Inch Nails.

In pop music, the song "Love Potion #9" was written by Jerry Leiber and Mike Stoller (who also wrote "Riot in Cell Block #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 other fields

• In Greek mythology there are nine Muses.