9's Magic.....

The Magic of Number 9

 

1.Finding the Digital Roots by Casting “9”

What is Digital root?  

If we add up the digits of a number until there is only one number left we have found what is called the digital root.  In other words, the sum of the digits of a number is called its digital root.

            Example:

            For 5674, 5 + 6 + 7 + 4 = 22 and 2 + 2 = 4

            »          4 is the digital root of 5674

One use of digital roots is for divisibility tests (like 3 and 9).  This method makes it easier to calculate the digital root.

Example:

Example:

            Find the digital root of 257520643

  

            Steps:

1. 2 + 7 = 9, cross out 2 and 7.

2.4 + 3 = 9, cross out 4, 3 and 2.

3.There are no other groups of numbers adding up to 9.

4.Add up the remaining digits, 5 + 5 + 0 + 3 = 13.

5.13 is more than 9, so 1 + 3 = 4.

6.The digital root is 4.

If there is nothing left after having cast out nines then the digital root is 9.

2. It will never let you go

Think of a two digit number, say 42, then subtract the reverse of its digits, 24, from 42

Choose any two digits number and for each one reverse the digits and subtract the smaller number from the larger.  Look at all the answers you get.  Do they all have a common divisor?  What do the digits sum to each time?  

Some Examples:

You see how fascinating and enjoying it is. In each case the difference is divisible by 9 (i.e. the common factor is 9) and the sum of the digits of the difference is always 9.

Do you think this will also work for three digit number or four-digit number.  Try it out!