Let's break down the problem step by step:
1. Performing Division:
We start with the division part of the expression:
[tex]\[
\frac{102.900}{12} = 8.575
\][/tex]
Here, the number [tex]\(102.900\)[/tex] has six significant figures, and [tex]\(12\)[/tex] has two significant figures. When dividing, the result must be rounded to the least number of significant figures in the given numbers, which is two significant figures. Thus, [tex]\(8.575\)[/tex] should be rounded to two significant figures:
[tex]\[
8.575 \approx 8.6
\][/tex]
2. Performing Multiplication:
Next, we calculate the multiplication part of the expression:
[tex]\[
170 \times 1.27 = 215.9
\][/tex]
Here, [tex]\(170\)[/tex] has three significant figures, and [tex]\(1.27\)[/tex] has three significant figures. When multiplying, the result should be rounded to the least number of significant figures in the given numbers, which is three significant figures:
[tex]\[
215.9 \approx 216
\][/tex]
3. Adding the Results:
Now we add the two results from the division and multiplication operations:
[tex]\[
8.6 + 216 = 224.6
\][/tex]
Finally, considering significant figures in the final result — the answer must match the least precise value used in the calculations. Here,
we take the smaller number of significant figures encountered from our earlier operations, which is two significant figures from the initial division step. Thus:
[tex]\[
224.6 \approx 220
\][/tex]
Therefore, expressed to the correct number of significant figures, the answer to
[tex]\[
(102.900 \div 12)+(170 \times 1.27)
\][/tex]
is [tex]\(220\)[/tex], and none of the provided answer choices (A, B, C, or D) match 220 exactly, meaning there might be a mistake in the choices themselves. Double-check the steps usually and ensure proper rounding.
