Eli5:Rule of nines?

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This is something I have been very interested in for a long time and have never found an answer to. If you multiply 9 at any number and then add the digits it will always come back to nine. I.E. 9 X 2 = 18
1+ 8 = 9. Nine is the only number I have found is the only number that does this. Any ideas why?

In: Mathematics

5 Answers

Anonymous 0 Comments

Just to reword the top comment into something more bite sized, the values that change when you add nine change by one, a value goes up by one, a value goes down by one. Start at 09. Add 9 to 09. The zero goes up one, the 9 goes down one, so you get 18. Now add 9 to that. The 1 goes up one, the 8 goes down one. Because you’re adding one and also subtracting one, it stays in an equalibrium of always equaling 9

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