Generally there is some sort of "trick" to do the problem in your head (or at least with minimal time on scratch paper). These generally involve estimating the answer to within a reasonable degree of certainty, and then noticing that only once answer choice is even close to that. If you post some problems that are giving you trouble I could see if I can help you out.
Just as an example though, say you need to solve 6.3X10^-5 = x^2.
You can rewrite it as 63X10^-6=x^2, and that's close enough to 64X10^-6. Now you just have to find the square root of two perfect squares, so x=8X10^-3. This is from a practice problem I did where the ultimate goal was the pH, and x was the concentration of hydrogen ions. Well, that's easy too: we now know the pH is between 3 and 2, but closer to 2. So whatever answer satisfies those criteria is the right one.
