Question

Using a number line, what whole number and rational number to the nearest half is 97−−√
between?

Answer 1

To find the whole number and the rational number to the nearest half that \( \sqrt{97} \) is between, we first need to calculate the approximate value of \( \sqrt{97} \).

1. **Estimate \( \sqrt{97} \)**:
- We know \( 9^2 = 81 \) and \( 10^2 = 100 \), so \( 9 < \sqrt{97} < 10 \).
- A more precise calculation can be done using a calculator or by approximation methods. We find:
\[
\sqrt{97} \approx 9.8488
\]

2. **Identify the whole number**:
- The whole number immediately less than \( 9.8488 \) is \( 9 \) and the one immediately greater is \( 10 \).
- Therefore, \( \sqrt{97} \) is between the whole numbers \( 9 \) and \( 10 \).

3. **Rational number to the nearest half**:
- The nearest half values around \( 9.8488 \) are \( 9.5 \) and \( 10.0 \).
- Since \( 9.8488 \) is closer to \( 10.0 \) than it is to \( 9.5 \), the rational number to the nearest half is \( 10.0 \).

**Conclusion**:
The whole number \( \sqrt{97} \) is between is \( 9 \) and \( 10 \), and the rational number to the nearest half is \( 10.0 \).