Properties of number 9

9 is a very powerful no. in maths. It has got max. properties which are useful in numerous ways. To start with-a very simple one. Addition of digits of no divisible by is also divisible by 9. e.g. consider 587646:- addition is 36 divisible by 9. For 36:- addition is 9.

Now when u add digits of a no.(no. of any length) and subtract addition from original no u get a no which divisible by 9. e.g. consider 58364 addition is 26. 58364-26=58338 its divisible by 9(check it if u want.)

Take a no. Add its digits. Now add 9 in original no. Again add the digits of addition. This addition and previous will be same. e.g. 69830 addition 8. Adding 9 we get 69839. Addition 8!

When u multiply by 9 or 99 or 999 etc:-
The multiplication is most simple. U just have to do is subtract 1 from that no, write it down. Then subtract given no from nearest power of 10 and write it down.
e.g. 8*9=8-1 | 10-8=72
278*999=278-1 | 1000-278 = 277722
This is because 9 or 99 or 999 is (10-1), (100-1), (1000-1)

Its very easy to find inverse of no ending with 9. Inverse of 9 is 0.11111111 That of 99 is 0.01010101 and of 999 is 0.001001001 etc.
For no containing other no than nine we can use following technique
Consider 1/29. For this first we need to write 0.0 then start dividing 10 with 3(2+1). While dividing for next no consider new remainder with new quotient.
e.g.
Method:-1/29=0. 0 3 4 4 8 2 7 5 8 6 2 0 6 8 9 6 5 5 1 7 2 4 1 3 7 9 3 1
Remainders are :-1 1 1 2 0 2 1 2 1 0 0 2 2 2 1 1 1 0 2 0 1 0 1 2 2 0 0 0

so the ans is 1/29=0.0344827586206896551724137931(recurring)

Hope I get some more to put here.