Sure! Let's go through each problem step-by-step and ensure we express the answers with the correct number of significant figures.
### Problem 1:
[tex]\[
\left(1.20 \times 10^4\right) \times \left(2.152 \times 10^2\right)
\][/tex]
1. Multiply the coefficients:
[tex]\[
1.20 \times 2.152 = 2.5824
\][/tex]
2. Multiply the powers of 10:
[tex]\[
10^4 \times 10^2 = 10^{4+2} = 10^6
\][/tex]
3. Combine the results:
[tex]\[
2.5824 \times 10^6
\][/tex]
4. Round to the appropriate number of significant figures:
The initial figures have significant figures as follows:
- [tex]\(1.20 \times 10^4\)[/tex] has 3 significant figures.
- [tex]\(2.152 \times 10^2\)[/tex] has 4 significant figures.
Therefore, we should round the result to 3 significant figures:
[tex]\[
2.58 \times 10^6
\][/tex]
Hence, the answer to the first problem is:
[tex]\[
2.582 \times 10^6
\][/tex]
### Problem 2:
[tex]\[
\frac{208}{5.3}
\][/tex]
1. Perform the division:
[tex]\[
208 \div 5.3 = 39.24528301886792
\][/tex]
2. Round to the appropriate number of significant figures:
The initial figures have significant figures as follows:
- 208 has 3 significant figures.
- 5.3 has 2 significant figures.
Therefore, we should round the result to 2 significant figures:
[tex]\[
39.245 \approx 39.2 (\text{rounded to 3 significant figures})
\][/tex]
Hence, the answer to the second problem is:
[tex]\[
39.2
\][/tex]
So, our final answers are:
[tex]\[
\begin{array}{l}
\left(1.20 \times 10^4\right) \times \left(2.152 \times 10^2\right) = 2.582 \times 10^6 \\
\frac{208}{5.3} = 39.2
\end{array}
\][/tex]
