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

Because it is one less than 10.

To add 9 and 9, you borrow one. Now 9 and 10 are being added. You gained 1 in the tens place and lost 1 in the ones place.

Repeat every time. Borrow 1, gain 1.

To be more baffled, look at the rule of 3.

Any number where the digits all add up to a number divisible by 3, is itself divisible by 3.

So, 163947261 is divisible by 3, I typed that randomly, then added a 1 at the end to make sure it met the rule of 3. I haven’t checked, but I know it will work out.

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