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Nine is an interesting natural number following 8 and preceding 10.

Multiply any natural number with 9, and if you sum the digits of the resultant value until it is just one number the answer will be always nine.

5 x 9 = 45(4 + 5 = 9)

8 x 9 =72(7 + 2 = 9)

104 x 9 = 936(9 + 3 + 6 = 18 =1 + 8 = 9)

8753634 x 9 = 78782706(7 + 8 +7 +8 + 2 + 7 + 0 + 6 = 45, 4 + 5 = 9)

78975134084 x 9 = 710776206756 = (7 + 1 + 0 + 7 + 7 + 6 + 2 + 0 + 6 + 7 + 5 + 6 = 54, 5 + 4 = 9)

Some other interesting facts involved in the multiples of nine are

12345679 x 9 = 111111111

12345679 x 18 = 222222222

12345679 x 81 = 999999999

Subtracting two base-10 positive integers that are transpositions of each other yields a number that is a whole multiple of nine. Examples:

64 – 46 = 18(1+8 = 9)

36957930 - 35967930 = 990000, (9+9 = 18, 1 + 8 = 9)

8965 – 5698 = 3267 (3 + 2 + 6 + 7 = 18, 1 + 8 = 9)

If you divide a number by the amount of 9s, corresponding to its number of digits, the number is turned into a repeating decimal. (e.g. 834/999 = 0.274274274274...)

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Daily Maths Topic Today - the magic of number nine.