Sure, let's go through each calculation step by step and determine the answer using the correct number of significant figures.
### Step 1: Multiplying 3.214 mm by 1.5 mm
Calculation:
[tex]\[
3.214 \, \text{mm} \times 1.5 \, \text{mm} = 4.821 \, \text{mm}^2
\][/tex]
Determining Significant Figures:
- 3.214 has 4 significant figures.
- 1.5 has 2 significant figures.
- When multiplying, the result should have the same number of significant figures as the number with the least significant figures, which is 2 in this case.
Rounding:
[tex]\[
4.821 \rightarrow 4.8 \, \text{mm}^2
\][/tex]
### Step 2: Dividing 13.702 L by 5 L
Calculation:
[tex]\[
13.702 \, \text{L} \div 5 \, \text{L} = 2.7404 \, \text{L}
\][/tex]
Determining Significant Figures:
- 13.702 has 5 significant figures.
- 5 has 1 significant figure.
- When dividing, the result should have the same number of significant figures as the number with the least significant figures, which is 1 in this case.
Rounding:
[tex]\[
2.7404 \rightarrow 3 \, \text{L}
\][/tex]
### Final Results:
1. When multiplying 3.214 mm by 1.5 mm:
- Result: [tex]\(4.8 \, \text{mm}^2\)[/tex]
2. When dividing 13.702 L by 5 L:
- Result: [tex]\(3 \, \text{L}\)[/tex]
So, the completed calculations with the correct number of significant figures are:
[tex]\[
\begin{array}{r}
3.214 \, \text{mm} \\
\times \quad 1.5 \, \text{mm} \\
\hline
4.8 \, \text{mm}^2 \\
\end{array}
\][/tex]
[tex]\[
13.702 \, \text{L} \div 5 \, \text{L} = 3 \, \text{L}
\][/tex]
