According to Einstein's theory of relativity, the maximum speed at which any information or matter can travel is the speed of light in a vacuum. This speed is considered a fundamental constant of nature.
Given the options, we must identify the one that correctly approximates the speed of light.
Here are the options once again:
1. [tex]$1.0 \times 10^7 \, \text{m/s}$[/tex]
2. [tex]$1.0 \times 10^8 \, \text{m/s}$[/tex]
3. [tex]$3.0 \times 10^8 \, \text{m/s}$[/tex]
4. [tex]$3.0 \times 10^9 \, \text{m/s}$[/tex]
The exact speed of light in a vacuum is approximately [tex]\(3.0 \times 10^8 \, \text{m/s}\)[/tex].
Let's verify each option:
1. [tex]$1.0 \times 10^7 \, \text{m/s}$[/tex] is one order of magnitude too small.
2. [tex]$1.0 \times 10^8 \, \text{m/s}$[/tex] is closer but still not quite right.
3. [tex]$3.0 \times 10^8 \, \text{m/s}$[/tex] is exactly the speed of light in a vacuum.
4. [tex]$3.0 \times 10^9 \, \text{m/s}$[/tex] is an order of magnitude too large.
Thus, the correct option, according to Einstein, is:
[tex]\[ \boxed{3.0 \times 10^8 \, \text{m/s}} \][/tex]
Therefore, the correct answer is the third option, [tex]\(3.0 \times 10^8 \, \text{m/s}\)[/tex].
Given the options, the third one correctly represents the approximate speed of light, beyond which nothing can move according to Einstein's theory. Consequently, the corresponding numerical answer is [tex]\(3\)[/tex].
