To determine between which pair of rational numbers \( \sqrt{18} \) lies, we first need to calculate \( \sqrt{18} \).
We know that:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]
Now we need to approximate \( \sqrt{2} \). The approximate value of \( \sqrt{2} \) is about 1.414. Therefore, we can calculate:
\[ \sqrt{18} \approx 3 \times 1.414 = 4.242 \]
Now, we can compare \( 4.242 \) with the given options.
- Between 4.2 and 4.3: \( 4.242 \) lies between \( 4.2 \) and \( 4.3 \).
- Between 4.3 and 4.5: \( 4.242 \) is not between \( 4.3 \) and \( 4.5 \) because \( 4.242 < 4.3 \).
- Between 8.9 and 9.1: \( 4.242 \) is not between \( 8.9 \) and \( 9.1 \) as it is much smaller.
- Between 9 and 9.2: \( 4.242 \) is not between \( 9 \) and \( 9.2 \) as it is also much smaller.
Thus, the correct answer is:
Between 4.2 and 4.3.