To find the whole number and rational number to the nearest half that \(\sqrt{97}\) is between, we first need to calculate the approximate value of \(\sqrt{97}\).
Calculating the square root:
\(\sqrt{97} \approx 9.849\)
Now we can see which whole numbers \(\sqrt{97}\) falls between. The perfect squares closest to 97 are \(81\) (which is \(9^2\)) and \(100\) (which is \(10^2\)).
This means:
\[ 9 < \sqrt{97} < 10 \]
Next, we find the rational number to the nearest half. The nearest halves around \(9.849\) are \(9.5\) and \(10.0\). Since \(9.849\) is closer to \(10\) than to \(9.5\), we round it to \(9.5\).
Thus, we conclude:
- The whole number \(\sqrt{97}\) is between is \(9\) and \(10\).
- The rational number to the nearest half that \(\sqrt{97}\) is closest to is \(10\).
So in summary:
\(\sqrt{97}\) is between the whole numbers \(9\) and \(10\), and the nearest half is \(10\).