1) The error occurred when you moved the decimal place one spot to the left without changing the exponent of 10 to go along with it.
Not changing the exponent will change the entire value of the answer. By changing 10.35 to 1.035, we made our answer 10 times smaller, so in order to compensate for that, we need to make 10^10 ten times bigger by changing it to 10^11.
2) 10.35 x 10^10 gets changed to:
1.035 x 10^11
3) The strategy we used is to apply proper scientific notation to our answer. We should recognize when we drastically change the value of our original answer.