To find the distance between the points \((9, 2)\) and \((3, 6)\), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \((x_1, y_1) = (9, 2)\) and \((x_2, y_2) = (3, 6)\).
Substituting the coordinates into the formula:
\[ d = \sqrt{(3 - 9)^2 + (6 - 2)^2} \]
Calculating the differences:
\[ 3 - 9 = -6 \implies (-6)^2 = 36 \] \[ 6 - 2 = 4 \implies 4^2 = 16 \]
Now substituting these values back into the distance formula:
\[ d = \sqrt{36 + 16} = \sqrt{52} \]
Now, we need to simplify \(\sqrt{52}\). We can factor it:
\[ \sqrt{52} = \sqrt{4 \times 13} = \sqrt{4} \times \sqrt{13} = 2\sqrt{13} \]
To find the numerical value of \(2\sqrt{13}\), we first approximate \(\sqrt{13}\):
\(\sqrt{13} \approx 3.60555\), so:
\[ 2\sqrt{13} \approx 2 \times 3.60555 \approx 7.2111 \]
Rounding to the nearest tenth, we get:
\[ 7.2 \]
Thus, the distance between the two points, rounded to the nearest tenth of a unit, is:
\[ \boxed{7.2} \text{ units} \]