Let's solve the problem step-by-step:
1. We are given two values: [tex]\(3.8 \times 10^3\)[/tex] and [tex]\(6.422 \times 10^5\)[/tex].
2. To determine how many times smaller [tex]\(3.8 \times 10^3\)[/tex] is compared to [tex]\(6.422 \times 10^5\)[/tex], we need to calculate the ratio of the larger value to the smaller value.
3. This means we divide [tex]\(6.422 \times 10^5\)[/tex] by [tex]\(3.8 \times 10^3\)[/tex].
[tex]\[
\text{Ratio} = \frac{6.422 \times 10^5}{3.8 \times 10^3}
\][/tex]
4. After performing this division, we obtain the ratio.
The result of this calculation shows how many times [tex]\(3.8 \times 10^3\)[/tex] fits into [tex]\(6.422 \times 10^5\)[/tex].
Given that the result of this calculation is [tex]\(169.0\)[/tex], we conclude that [tex]\(3.8 \times 10^3\)[/tex] is 169 times smaller than [tex]\(6.422 \times 10^5\)[/tex].
Therefore, the correct option is:
[tex]\[
169
\][/tex]
