To determine the whole number and the rational number to the nearest half that \( \sqrt{10} \) (which is what \( 10^{-1/2} \) represents) is between, let's first calculate \( \sqrt{10} \).
Calculating \( \sqrt{10} \):
\[ \sqrt{10} \approx 3.162 \]
Next, we need to find the whole number it is between:
- The whole number right below \( 3.162 \) is \( 3 \).
- The whole number right above \( 3.162 \) is \( 4 \).
Now, let's find the rational number to the nearest half. The nearest halves around \( 3.162 \) are \( 3.0 \) and \( 3.5 \).
Since \( 3.162 \) is closer to \( 3.0 \) than to \( 3.5 \), we say:
\[ \sqrt{10} \text{ is between } 3 \text{ and } 3.5. \]
So the final answer is:
\( \sqrt{10} \) is between 3 and 3.5.
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