To locate the point [tex]\(\frac{13}{6}\)[/tex] on the number line, we need to understand what this fraction represents when expressed as a decimal.
The fraction [tex]\(\frac{13}{6}\)[/tex] simplifies to approximately [tex]\(2.1666666666666665\)[/tex].
We can rewrite this as [tex]\(2 + 0.1666666666666665\)[/tex], which indicates that [tex]\(\frac{13}{6}\)[/tex] is a little more than [tex]\(2\)[/tex].
A quick verification involves recognizing that:
- [tex]\(\frac{12}{6} = 2\)[/tex]
- [tex]\(\frac{14}{6} \approx 2.333...\)[/tex]
This implies [tex]\(\frac{13}{6}\)[/tex] falls between [tex]\(2\)[/tex] and [tex]\(2.333...\)[/tex] on the number line. Given this range, the specific point closer to [tex]\(\frac{13}{6}\)[/tex] is point [tex]\(2.1666666666666665\)[/tex].
Therefore, the point at [tex]\(\frac{13}{6}\)[/tex] on the number line is [tex]\(C).
Thus the correct choice is \(C\)[/tex].
