## Nine is a Magic Number

I’m going to tell you about the magic that is accomplished in Microsoft Word when you push the Magic F9 key.
But first, I want to impress you with how cosmically wonderful the number nine is.

When you multiply nine by any number and add up the digits of the answer, you get 9.
Examples:
2 × 9 = 18  (1 + 8 = 9)
3 × 9 = 27  (2 + 7 = 9)
9 × 9 = 81  (8 + 1 = 9)
234 × 9 = 2106 (2 + 1 + 0 + 6 = 9)

The step in parentheses is called “finding the digital root,” which means repeatedly adding the digits of the answer until it is pared down to just one digit.
482729235601 × 9 = 4344563120409
(4 + 3 + 4 + 4 + 5 + 6 + 3 + 1 + 2 + 0 + 4 + 0 + 9 = 45) then (4 + 5 = 9)

The difference between a positive integer and the sum of its digits (or digital root) is a multiple of nine.
For example, the sum of the digits of 41 is 5, and 41-5 = 36. The digital root of 36 is 3+6 = 9, which means it is evenly divisible by nine.

Subtracting two positive integers that are transpositions of each other yields a number that is a whole multiple of nine.
For example, 41-14 = 27. The digital root of 27 is 2+7 = 9, therefore 27 is a multiple of 9.

My fourth grade teacher, a nun named Sister Mary Carmen, wowed the whole class when she taught us a trick for checking our math using a technique called “Crossing Out Nines.” You cross out numbers that add up to 9 horizontally, then pare what’s left down to the “digital root,” then add those up vertically to see if they are the same as the digital root of the sum (or difference – this method works with subtraction, too.)

284656903  Cross out the 9, 5+4, 6+3, left with 2+8+6+0=16,      1+6= 7
138957265  Cross out the 9, 7+2, 6+3, 1+8, left with 5+5=10,      1+0= 1
+234857263  Cross out the 7+2, 6+3, 5+4, left with 2+3+8=13,     1+3= 4
658471431  Cross out the 7+1+1, 6+3, 5+4, left with 8+4=12                   12

Nine is the binary complement of number six:
9 = 1001
6 = 0110
and when upside-down, the number nine looks just like the number six.

How cool is that? We won’t even go into the Beatles song called “Revolution Nine.”

But now, back to the totally cool F9 key in Microsoft Word.
If you are numbering your sections, tables and figures in a large document and need to insert some new ones in between some that are already numbered, just add them in the proper format, then Select All and push F9, and Presto-Change-O! All your numbered items are magically renumbered.
That’s a handy little feature, right there, eh?

### 2 Responses to “Nine is a Magic Number”

1. Number 9, number 9 « CyberText Newsletter Says:

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2. Nine is a magic number! East Park parkrun encompassing all… | Running Scared Says:

[…] Park parkrun here I come!  I was joining them for their ninth event. By the way, did you know nine is a magic number of cosmic wonder?  For […]