To solve the given problem, we'll break it down into two parts.
### Part 1: Multiplication and Scientific Notation
First, we want to compute the product of two numbers expressed in scientific notation:
[tex]\[
(1.20 \times 10^4) \times (2.152 \times 10^2)
\][/tex]
1. Multiply the coefficients:
[tex]\[
1.20 \times 2.152 = 2.5824
\][/tex]
2. Add the exponents:
[tex]\[
10^4 \times 10^2 = 10^{4+2} = 10^6
\][/tex]
Thus, the product can be expressed as:
[tex]\[
(1.20 \times 10^4) \times (2.152 \times 10^2) = 2.5824 \times 10^6
\][/tex]
To check the original multiplication without considering scientific notation:
1. [tex]\[
1.20 \times 10^4 = 12000
\][/tex]
2. [tex]\[
2.152 \times 10^2 = 215.2
\][/tex]
3. [tex]\[
12000 \times 215.2 = 2582400.0
\][/tex]
Therefore:
[tex]\[
2582400.0 = 2.5824 \times 10^6
\][/tex]
We find that \( C = 2.5824 \).
### Part 2: Division
Second, we need to calculate the division:
[tex]\[
\frac{208}{5.3}
\][/tex]
Perform the division:
[tex]\[
\frac{208}{5.3} \approx 39.24528301886792
\][/tex]
Thus, the steps give the final answers:
1. \((1.20 \times 10^4) \times (2.152 \times 10^2) = 2.5824 \times 10^6\)
2. \(\frac{208}{5.3} \approx 39.24528301886792\)
Conclusively, filling in the squares, we get:
[tex]\[
\begin{array}{l}
(1.20 \times 10^4) \times (2.152 \times 10^2) = 2.5824 \times 10^6 \\
\frac{208}{5.3} = 39.24528301886792
\end{array}
\][/tex]
