When doing multiple calculations with significant figures, use the rules of significant figures through each calculation and then round only at the very end. You should not round each number after every calculation as this will introduce and propagate error. When multiplying or dividing, the answer should have the same number of significant figures as the number with the smallest number of significant figures. When adding or subtracting, the answer should have the same number of decimal places as the number with the smallest number of decimal places.
In your example above you are correct. Both numbers have 3 decimal places so the answer should have 3 decimal places as well even though it drops from 3 to 2 significant figures. You continue with the 2 significant figures. But remember, the number of significant figures could go back up to 3 if you added or subtracted another number to it with 3 decimal places that included no zeros.