9.99x10 ^-2 + 1.11 × 10^-2 i dont have the same scientific calculator as the one from school. would like to verify my math is correct

The answer should not depend on which machine or which pencil you use to
find it.  If you work a problem two different ways and get two different answers,
then at least one of them is wrong, and there's a pretty good chance that both
of them are.

(9.99 of anything) + (1.11 of the same thing) = 11.1 of them

9.99 (x 10^-2) + 1.11 (x 10^-2) = 11.1 (x 10^-2) .

Can we do any more with that ?

10^-2  =  1 / 10^2  =  1 / 100 .

11.1 x 10^-2  =  11.1 / 100  =  0.111

Not sure what the question is?