Nine

The nine (9) is the natural number that follows 8 and precedes 10.

A sign with number nine on a street.

• It is a composite number, which has the following factors: 1 and 3. And since the sum of its factors is 4 ≤ 9, it is a defective number.
• The 9th prime number is 23.
• 9 is the square of 3.
• Eneagone is a polygon of 9 sides and 9 interior angles.
• First number of composite luck.
• His square is 81, his cube is 729.
• 9 is the highest single digit number in the decimal system.
• 9 is the only positive power that is one more than another positive power, according to the Catalan Conjecture.
• In the ternary system is written 100₃
• It is the first type number (p1 + 2 = p2 - 2). The lower and immediate prime number to 9 is 7 and the highest and immediate prime number is 11. Both are at the same distance: 7+2=9; 11-2=9
• Motzkin's number.
• Kaprekar number.
• A sequence of six 9 occurs in the decimal representation of the number pi (π), beginning in the 762 decimal place. It's also called Feynman's point.
• Like 9 = 3 ^{2 1}It's an exponential factor.
• It is a term of the succession of Padovan.
• A refactorable number.
• It's a self-number.

Digital root of a number

If we add all the digits in a number, and then all the digits in the sum, and continue until we reach a single-digit number, we get the digital root of the initial number.

Logically, any natural number that contains one or more nines as one of its digits, the sum of its digits (and, if necessary, those of the number resulting from the addition, until the result is a one-digit number) will give an identical result to the addition of the same digits if the number nine is not present.

Example: 19 => 1 + 9 = 10 => 1 + 0 = 1

The same thing happens, if the number contains more nines:

In the natural number 123456789, the sum of the constituent digits added individually will be identical to the sum of the digits in the number 12345678; because 1 + 2 + 3 ++…+ 8 + 9 = 45, and 4 + 5 = 9 gives the same result as 1 + 2 + 3 +…+ 7 + 8 = 36, and 3 + 6 = 9

This property is used to check the certainty of the result in multiplications and divisions, using the test of nine.

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 only 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)

Science

• Atomic fluoride (F).
• Messier M9 object is a globular cluster of Ofiuco constellation.
• Before 2006 (when Pluto was officially designated as a non-planet), there were nine planets in the solar system.
• A human pregnancy usually lasts nine months.

References and notes