Sure, here is the step-by-step solution to the given expression:
Given the expression:
[tex]\[
\frac{(34.123 + 1.10)}{(98.7654 - 7.494)}
\][/tex]
### Step 1: Perform the Addition in the Numerator
First, we need to add the numbers in the numerator:
[tex]\[
34.123 + 1.10 = 35.223
\][/tex]
### Step 2: Perform the Subtraction in the Denominator
Next, we need to subtract the numbers in the denominator:
[tex]\[
98.7654 - 7.494 = 91.2714
\][/tex]
### Step 3: Perform the Division
Having calculated the numerator and the denominator, we can now perform the division:
[tex]\[
\frac{35.223}{91.2714} = 0.385914974460784
\][/tex]
### Step 4: Determine the Significant Figures
When recording the answer with the correct number of significant figures, we need to look at the significant figures of the numbers used in the calculation. The number of significant figures in 34.123 is 5, in 1.10 is 3, in 98.7654 is 7, and in 7.494 is 4. The result of the addition in the numerator and the subtraction in the denominator should be rounded to match the least number of significant figures. However, since we are focusing on the final result, the least number of significant figures in our calculation components are 4 (from the denominator calculation).
Thus, we round our final result to 4 significant figures:
[tex]\[
0.3859
\][/tex]
### Final Answer
So, the answer to the expression with the correct number of significant figures is:
[tex]\[
\boxed{0.3859}
\][/tex]
