Answer :
Certainly! Let's break down the problem step by step to find the answer with the correct number of significant figures:
1. Calculate each component separately:
- First, calculate [tex]\(3.53 \times 0.0840\)[/tex]:
- This results in [tex]\(0.29652\)[/tex], and both numbers have three significant figures. The result should also have three significant figures: [tex]\(0.297\)[/tex].
- Next, calculate [tex]\(14.8 \times 0.046\)[/tex]:
- This results in [tex]\(0.6808\)[/tex]. Here, [tex]\(14.8\)[/tex] has three significant figures, and [tex]\(0.046\)[/tex] has two significant figures. Therefore, the result should have two significant figures: [tex]\(0.68\)[/tex].
2. Perform the calculations in sequence:
- Subtract the second result from the first:
- [tex]\(0.297 - 0.68 = -0.383\)[/tex].
- Then, add [tex]\(39.011\)[/tex] to the above result:
- [tex]\(-0.383 + 39.011 = 38.628\)[/tex].
3. Determine the correct number of significant figures:
- For addition and subtraction, the result should be rounded to the least number of decimal places from the numbers being added or subtracted.
- Here, [tex]\(-0.383\)[/tex] and [tex]\(39.011\)[/tex] have three decimal places, so the result should also be rounded to three decimal places: [tex]\(38.628\)[/tex].
Considering all the steps and significant figures, the final answer is [tex]\(38.63\)[/tex] when rounded to three decimal places. So, the correct choice is 38.63.
1. Calculate each component separately:
- First, calculate [tex]\(3.53 \times 0.0840\)[/tex]:
- This results in [tex]\(0.29652\)[/tex], and both numbers have three significant figures. The result should also have three significant figures: [tex]\(0.297\)[/tex].
- Next, calculate [tex]\(14.8 \times 0.046\)[/tex]:
- This results in [tex]\(0.6808\)[/tex]. Here, [tex]\(14.8\)[/tex] has three significant figures, and [tex]\(0.046\)[/tex] has two significant figures. Therefore, the result should have two significant figures: [tex]\(0.68\)[/tex].
2. Perform the calculations in sequence:
- Subtract the second result from the first:
- [tex]\(0.297 - 0.68 = -0.383\)[/tex].
- Then, add [tex]\(39.011\)[/tex] to the above result:
- [tex]\(-0.383 + 39.011 = 38.628\)[/tex].
3. Determine the correct number of significant figures:
- For addition and subtraction, the result should be rounded to the least number of decimal places from the numbers being added or subtracted.
- Here, [tex]\(-0.383\)[/tex] and [tex]\(39.011\)[/tex] have three decimal places, so the result should also be rounded to three decimal places: [tex]\(38.628\)[/tex].
Considering all the steps and significant figures, the final answer is [tex]\(38.63\)[/tex] when rounded to three decimal places. So, the correct choice is 38.63.
