| Number: | 9 |
| Numeral: | nonary |
| Divisor: | 1,3,9 |
| Roman: | IX, ix |
| Greek Prefix: | ennea- |
| Latin Prefix: | nona- |
| Lang1: | Amharic |
| Lang1 Symbol: | ፱ |
| Lang2: | Arabic, Kurdish, Persian, Sindhi, Urdu |
| Lang4: | Armenian numeral |
| Lang5: | Bengali |
| Lang6: | Chinese numeral |
| Lang6 Symbol: | 九, 玖 |
| Lang7: | Devanāgarī |
| Lang8: | Santali |
| Lang9: | Greek numeral |
| Lang9 Symbol: | θ´ |
| Lang10: | Hebrew numeral |
| Lang11: | Tamil numerals |
| Lang12: | Khmer |
| Lang12 Symbol: | ៩ |
| Lang13: | Telugu script |
| Lang14: | Thai numeral |
| Lang15: | Malayalam |
| Lang15 Symbol: | ൯ |
| Lang16: | Babylonian numeral |
| Lang17: | Egyptian hieroglyph |
| Lang18: | Morse code |
| Lang19: | NATO phonetic alphabet |
| Lang19 Symbol: | NINER |
9 (nine) is the natural number following and preceding .
See also: Hindu–Arabic numeral system. Circa 300 BC, as part of the Brahmi numerals, various Indians wrote a digit 9 similar in shape to the modern closing question mark without the bottom dot. The Kshatrapa, Andhra and Gupta started curving the bottom vertical line coming up with a -look-alike.[1] How the numbers got to their Gupta form is open to considerable debate. The Nagari continued the bottom stroke to make a circle and enclose the 3-look-alike, in much the same way that the sign @ encircles a lowercase a. As time went on, the enclosing circle became bigger and its line continued beyond the circle downwards, as 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.
While the shape of the glyph for the digit 9 has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in .
The form of could possibly derive from the Arabic letter waw, which in its isolated form (و) resembles the number 9.
The modern digit resembles an inverted 6. To disambiguate the two on objects and labels that can be inverted, they are often underlined. It is sometimes handwritten with two strokes and a straight stem, resembling a raised lower-case letter q, which distinguishes it from the 6. Similarly, in seven-segment display, the number 9 can be constructed either with a hook at the end of its stem or without one. Most LCD calculators use the former, but some VFD models use the latter.
9 is the fourth composite number, and the first odd composite number. 9 is also a refactorable number.[2]
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers in decimal, a method known as long ago as the 12th century.[3]
9 is the only square number that is the sum of two consecutive, positive cubes:
32=9=13+23
If an odd perfect number exists, it will have at least nine distinct prime factors.[5]
9 is the sum of the cubes of the first two non-zero positive integers
13+23
n
\Q\left[\sqrt{-n}\right]
The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
A polygon with nine sides is called a nonagon.[8] A regular nonagon can be constructed with a regular compass, straightedge, and angle trisector.[9]
The lowest number of squares needed for a perfect tiling of a rectangle is 9.
| Division | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 9 ÷ x | 9 | 4.5 | 3 | 2.25 | 1.8 | 1.5 | 1. | 1.125 | 1 | 0.9 | 0. | 0.75 | 0. | 0.6 | 0.6 | |
| x ÷ 9 | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 0. | 1 | 1. | 1. | 1. | 1. | 1. | 1. |
| Exponentiation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 9 | 9 | 81 | 729 | 6561 | 59049 | 531441 | 4782969 | 43046721 | 387420489 | 3486784401 | |
| x | 1 | 512 | 19683 | 262144 | 1953125 | 10077696 | 40353607 | 134217728 | 387420489 | 1000000000 |
Nine is a number that appears often in Indian culture and mythology.[10] For example, there are nine influencers attested to in Indian astrology. In the Vaisheshika branch of Hindu philosophy, there are nine universal substances or elements: Earth, Water, Air, Fire, Ether, Time, Space, Soul, and Mind.[11] Navaratri is a nine-day festival dedicated to the nine forms of Durga.[12] [13]
Nines are a notation for expressing the purity of a chemical.
In chemical nomenclature, the prefix "non-" stands for the number nine, for example in molecular chains with nine atoms such as "nonane" for an alkane with nine carbon atoms. The prefixes play a role in the naming of molecules, especially in organic chemistry to indicate the number of similar atoms or groups in the molecule (e.g. "nonan" for 9 carbon atoms, "nonavalent" for nine-valent. Nonapeptides are peptides that consist of nine amino acids.
9 is a common terminal digit in psychological pricing.
