Hello 
How much water must be added to 100mL of a solution of a strong base of pH 13.0 in order to decrease the pH to 11.0?
I tried subbing in the H+ concentrations using the c1 x v1 = c2 x v2 formula:
10^(-13) x 0.1 = 10^(-11) x v2
v2 = 0.001 L
So yeah obviously my answer is wrong lol
Thankyou 
Alright, so your method is on the right track BUT since we're dealing with bases your concentration in the equation must be of [OH-] rather than [H+]. Likewise, if you're dealing with acids, the concentration in the equation should be kept as [H+] rather than [OH-]. Think about the reason for this mathematically...
[H+] in the original solution = 10^-13 so [OH-] = 10^-1
[H+] in the diluted solution = 10^-11 so [OH-] = 10^-3
c1v1=c2v2 since we're dealing with dilutions.
10^-1*0.1=10^-3*v2
v2=10
Since we have 100mL already, we need to add 10-0.1=9.9L