Hey guys! Thanks for any help in advance! I'm back with this problem:

Question

Calculate the percent dissociation for a 1.00 × 10-6 M solution of HCN at 25 °C.
Ka = 4.90 × 10-10.
So my question really is do I have to use water when I calculate the percent dissociation because my teacher said that at a certain point if it is so small you'll have to use water?
Here is my maybe answer:
I did this two ways, 1 with and 1 without water
Way 1 (Without water)
1,00*10^-6M 0M 0M
-x x x
1.00*10^-6-x x x
x^2/1.00*10^-6-x=4.9*10^-10
-x^2-4.9*10^-10+4.9*10^-16=0
x=2.19*10^-8
2.19*10^-8/1.00*10^-6*100=2.19%

Way 2 (With Water)
1.00*10^-6M 1.00*10^-7M 0M
-x x x
1.00*10^-6-x 1.00*10^-7+x x
x(1.00*10^-7+x)/(1.00*10^-6-x)=4.9*10^-10
-x^2-1.0049*10^-7+4.9*10^-16=0
x=(4.66*10^-9/1.00*10^-6)*100=.466%

There is a big difference between those two numbers, so does that mean I did it wrong, or does that mean that you have to factor the value of water in for the H+ ions because the M is so small?