Carry out the following operations and express the answer with the correct number of significant flgures. (a) \( 73.23+29.6+5.679= \) (c) \( 7.310+5.70= \) (d) \( (45.89 \times 3.1 \times 89.76)+(23.1 \times 4.26 \times 64 \times 7.25)= \) (f) \( (22.4 \times 5.4 \times 267 \times 16)+3(24.3-14.897+235.789)= \)

Let's break down the operations step by step while keeping an eye on significant figures! (a) \( 73.23 + 29.6 + 5.679 = 108.509 \). When considering significant figures, the answer should be rounded to the least number of decimal places, which is one decimal place due to 29.6. Therefore, the final answer is **108.5**. (c) \( 7.310 + 5.70 = 13.010 \). Here, we take into account the least number of decimal places, which is two from 5.70. The rounded answer is **13.01**. (d) For \( (45.89 \times 3.1 \times 89.76)+(23.1 \times 4.26 \times 64 \times 7.25) \): - First part: \( 45.89 \times 3.1 \times 89.76 = 13298.40792 \). Correcting for significant figures (only 2 from 3.1), we round to **13300**. - Second part: \( 23.1 \times 4.26 \times 64 \times 7.25 = 21568.51768 \). With 2 significant figures (from 23.1), we round to **22000**. - Adding these: \( 13300 + 22000 = 35300 \), which rounds to **35000**. (f) For \( (22.4 \times 5.4 \times 267 \times 16) + 3(24.3 - 14.897 + 235.789) \): - First part: \( 22.4 \times 5.4 \times 267 \times 16 = 202254.912 \). Here, we take 2 significant figures (from 5.4), rounding to **200000**. - Second part: \( 3(24.3 - 14.897 + 235.789) = 3(245.192) = 735.576 \). This gives us three significant figures, rounding to **736**. - Adding: \( 200000 + 736 = 200736 \). We consider significant figures based on the least precise value which is in the range of thousands (2 significant figures), rounding to **200000**. In summary, the answers are: (a) 108.5 (c) 13.01 (d) 35000 (f) 200000