its is 9.
ACCORDING TO WIKIPEDIA
9
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This article is about the number. For the year, see AD 9. For other uses, see 9 (disambiguation) and Number nine (disambiguation).
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List of numbers — Integers
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Cardinalnine
Ordinal9th
(ninth)
Numeral systemnonary
Factorization32
Divisors1, 3, 9
Greek numeralΘ´
Roman numeralIX, ix
Greek prefixennea-
Latin prefixnona-
Binary10012
Ternary1003
Octal118
Duodecimal912
Hexadecimal916
Amharic፱
Arabic, Kurdish, Persian, Sindhi, Urdu٩
Armenian numeralԹ
Bengali৯
Chinese numeral九, 玖
Devanāgarī९
Greek numeralθ´
Hebrew numeralט
Tamil numerals௯
Khmer៩
Telugu numeral౯
Thai numeral๙
Look up nine in Wiktionary, the free dictionary.
9 (nine) is the natural number following 8 and preceding 10.
Contents
1Mathematics
2List of basic calculations
3Evolution of the glyph
4Alphabets and codes
5Commerce
6Culture and mythology
6.1Indian culture
6.2Chinese culture
6.3Ancient Egypt
6.4European culture
6.5Greek mythology
6.6Mesoamerican mythology
6.7Aztec mythology
6.8Mayan mythology
7Anthropology
7.1Idioms
7.2Society
7.3Technique
8Literature
9Organizations
10Places and thoroughfares
11Religion and philosophy
12Science
12.1Astronomy
12.2Chemistry
12.3Physiology
13Sports
14Technology
15Music
16See also
17References
18Further reading
Mathematics
9 is a composite number, its proper divisors being 1 and 3. It is 3 times 3 and hence the third square number. Nine is a Motzkin number.[1] It is the first composite lucky number, along with the first composite odd number and only single-digit composite odd number.
9 is the only positive perfect power that is one more than another positive perfect power, by Mihăilescu's Theorem.
9 is the highest single-digit number in the decimal system. It is the second non-unitary square prime of the form (p2) and the first that is odd. All subsequent squares of this form are odd.
Since 9 = 321, 9 is an exponential factorial.[2]
A polygon with nine sides is called a nonagon or enneagon.[3] A group of nine of anything is called an ennead.
In base 10, a positive number is divisible by 9 if and only if its digital root is 9.[4] That is, if any natural number is multiplied by 9, and the digits of the answer are repeatedly added until it is just one digit, the sum will be nine:
2 × 9 = 18 (1 + 8 = 9)
3 × 9 = 27 (2 + 7 = 9)
9 × 9 = 81 (8 + 1 = 9)
121 × 9 = 1089 (1 + 0 + 8 + 9 = 18; 1 + 8 = 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)
There are other interesting patterns involving multiples of nine:
12345679 × 9 = 111111111
12345679 × 18 = 222222222
12345679 × 81 = 999999999
This works for all the multiples of 9. n = 3 is the only other n > 1 such that a number is divisible by n if and only if its digital root is divisible by n. 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.
The difference between a base-10 positive integer and the sum of its digits is a whole multiple of nine. Examples:
The sum of the digits of 41 is 5, and 41 − 5 = 36. The digital root of 36 is 3 + 6 = 9, which, as explained above, demonstrates that it is divisible by nine.
The sum of the digits of 35967930 is 3 + 5 + 9 + 6 + 7 + 9 + 3 + 0 = 42, and 35967930 − 42 = 35967888. The digital root of 35967888 is 3 + 5 + 9 + 6 + 7 + 8 + 8 + 8 = 54, 5 + 4 = 9.
Casting out nines is a quick way of testing the calculations of sums, differences, products, and quotients of integers, known as long ago as the 12th century.[5]
Six recurring nines appear in the decimal places 762 through 767 of π, see Six nines in pi.
If dividing a number by the amount of 9s corresponding to its number of digits, the number is turned into a repeating decimal. (e.g.
274
/
999
= 0.274274274274...)
There are nine Heegner numbers.[6]
List of basic calculations
Multiplication123456789102025501001000
9 × x91827364554637281901802254509009000
Division123456789101112131415
9 ÷ x94.532.251.81.51.2857141.12510.90.810.750.6923070.64285710.6
'x ÷ 90.10.20.30.40.50.60.70.811.11.21.31.41.51.6
Exponentiation12345678910
9x9817296561590495314414782969430467213874204893486784401
x9151219683262144195312510077696403536071342177283874204891000000000
Radix151015202530405060708090100
1101201301401502002505001000100001000001000000
x91511916922927933944955966977988911091219
1329143915491659176924293079615913319146419162151917836619
