If you eliminate 90% of bacteria with the first application, then 10% of the bacteria will survive.
If you eliminate another 90% of bacteria remaining with the first application, then you will take 90% of 10 and subtract that to find the population remaining after the second application.
[tex].90 * .10 = .09[/tex]
[tex].10 - .09 = .01[/tex]
Only 1% of the bacteria is left. Therefore, 99% of the bacteria has been eliminated.