Final answer:
Calculating operations with the correct number of sig figs involves applying rules for each arithmetic step, being guided by the number with the least sig figs, and rounding the final answer accordingly.
Step-by-step explanation:
Performing each calculation with the correct number of significant figures (sig figs) is essential in mathematics and science for precision and accuracy. Here's how we solve each part of the student's question:
- For part A: (24.6681 x 2.38) + 332.58, the multiplication step limits sig figs to 3 (due to 2.38), giving us 58.71 as an intermediate step. Adding 332.58, which has 5 sig figs, should yield a final answer rounded to 3 sig figs, which are dictated by the least number of sig figs from the multiplication step, resulting in 391.
- For part B: (85.3 - 21.489) x 0.0059, we start with the subtraction step yielding 63.811 (limited by 85.3 to 3 sig figs). Multiplication by 0.0059 (with 2 sig figs) leads to a final answer rounded to 2 sig figs, which is 0.38.
- For part C: (512/986.7) + 5.44, division yields a number with as many sig figs as the least precise number (512 with 3 sig figs). Thus, we get 0.51899, which, when added to 5.44 (with 3 sig figs), gives a final answer of 5.96.
- For part D: [(28.7 x 10⁵)/48.533] + 144.99, the division step is limited by 28.7 with 3 sig figs, yielding an intermediate answer of about 59130. Adding 144.99 with 5 sig figs results in a final answer with 3 sig figs, making it 59200.