9 is the natural number following and preceding.


9 is a composite number, its proper divisors being and. It is 3 times 3 and hence the third square number. Nine is a Motzkin number. 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 and the first that is odd. All subsequent squares of this form are odd.
Since, 9 is an exponential factorial.
A polygon with nine sides is called a nonagon or enneagon. 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. 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:
There are other interesting patterns involving multiples of nine:
This works for all the multiples of 9. is the only other 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 have this property. Another consequence of 9 being, 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:
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.
Six recurring nines appear in the decimal places 762 through 767 of pi|, 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.
There are nine Heegner numbers.


In probability, the nine is a logarithmic measure of the probability of an event, defined as the negative of the base- 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 of probability. Zero probability gives zero nines. A 100% probability is considered to be impossible in most circumstances: that results in infinite improbability. The effectivity of processes and the availability of systems can be expressed as a series of "nines". For example, "five nines" availability implies a total downtime of no more than five minutes per year – typically a very high degree of :wikt:reliability|reliability; but never 100%.

List of basic calculations

9 ÷ x94.532.
'x ÷



Evolution of the glyph

According to Georges Ifrah, the origin of the 9 integers can be attributed to ancient Indian civilization, and was adopted by subsequent civilizations in conjunction with the.
In the beginning, various Indians wrote 9 similar 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. The Nagari continued the bottom stroke to make a circle and 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, 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 9 character has an ascender in most modern typefaces, in typefaces with text figures the character usually has a descender, as, for example, in.
This numeral resembles an inverted 6. To disambiguate the two on objects and documents that can be inverted, the 9 is often underlined, as is done for the 6. Another distinction from the 6 is that it is sometimes handwritten with a straight stem, resembling a raised lower-case letter q.

Alphabets and codes

Indian culture

Nine is a number that appears often in Indian culture and mythology. Some instances are enumerated below.



A human pregnancy normally lasts nine months, the basis of Naegele's rule.