Answer :
To solve the problem and determine the correct answer with the appropriate number of significant figures, follow these steps:
1. Perform the Calculation Inside the Parentheses:
We start by calculating the expression inside the parentheses:
[tex]\[
12.02 - 11.52 = 0.50
\][/tex]
In this subtraction, both numbers (12.02 and 11.52) have two decimal places, resulting in the answer having two decimal places as well.
2. Multiply the Result by 78.222:
Next, multiply the result from step 1 by 78.222:
[tex]\[
78.222 \times 0.50 = 39.111
\][/tex]
3. Determine the Correct Number of Significant Figures:
In multiplication, the number of significant figures in the result is determined by the number in the calculation with the fewest significant figures. The numbers are:
- 78.222 has 5 significant figures.
- 0.50 has 2 significant figures.
Therefore, the result must be expressed with 2 significant figures.
4. Round the Result:
Round 39.111 to 2 significant figures:
[tex]\[
39.111 \approx 39
\][/tex]
5. Select the Correct Answer:
The correctly rounded result, based on significant figures, is 39. Therefore, the answer to the question is:
39
1. Perform the Calculation Inside the Parentheses:
We start by calculating the expression inside the parentheses:
[tex]\[
12.02 - 11.52 = 0.50
\][/tex]
In this subtraction, both numbers (12.02 and 11.52) have two decimal places, resulting in the answer having two decimal places as well.
2. Multiply the Result by 78.222:
Next, multiply the result from step 1 by 78.222:
[tex]\[
78.222 \times 0.50 = 39.111
\][/tex]
3. Determine the Correct Number of Significant Figures:
In multiplication, the number of significant figures in the result is determined by the number in the calculation with the fewest significant figures. The numbers are:
- 78.222 has 5 significant figures.
- 0.50 has 2 significant figures.
Therefore, the result must be expressed with 2 significant figures.
4. Round the Result:
Round 39.111 to 2 significant figures:
[tex]\[
39.111 \approx 39
\][/tex]
5. Select the Correct Answer:
The correctly rounded result, based on significant figures, is 39. Therefore, the answer to the question is:
39
