To find a rational number that is between \(\sqrt{10}\) and \(\sqrt{11}\), we first need to determine the approximate values of \(\sqrt{10}\) and \(\sqrt{11}\).
- \(\sqrt{10} \approx 3.162\)
- \(\sqrt{11} \approx 3.317\)
Now, we need to select a number between 3.162 and 3.317 from the given options:
- \( \frac{10}{3} \approx 3.333\) (which is greater than \(\sqrt{11}\))
- \(3.1\) (which is between \(\sqrt{10}\) and \(\sqrt{11}\))
- \(3.4\) (which is greater than \(\sqrt{11}\))
- \(\frac{16}{5} = 3.2\) (which is also between \(\sqrt{10}\) and \(\sqrt{11}\))
Based on this evaluation, both \(3.1\) and \(\frac{16}{5}\) are rational numbers that lie between \(\sqrt{10}\) and \(\sqrt{11}\).
Thus, one example of a rational number that is definitely between \(\sqrt{10}\) and \(\sqrt{11}\) is \(3.1\).