Step 1 :Given the data set of the number of hazardous waste sites in a sample of states of the United States in a recent year: 0, 2, 3, 6, 9, 9, 9, 12, 12, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 19, 20, 21, 25, 26, 29, 30, 32, 38, 97, 116.
Step 2 :The first quartile (Q1) is the middle number between the smallest number and the median of the data set.
Step 3 :The third quartile (Q3) is the middle value between the median and the highest value of the data set.
Step 4 :By calculating, we find that the first quartile (Q1) is 12 and the third quartile (Q3) is 24.
Step 5 :Final Answer: The first quartile of these data is \(\boxed{12}\). The third quartile of these data is \(\boxed{24}\).