To find the diameter of a circle given the circumference, you can use the formula:
\[ C = \pi \times d \]
where \( C \) is the circumference and \( d \) is the diameter.
In this case, the circumference \( C \) is 27 mm. Rearranging the formula gives:
\[ d = \frac{C}{\pi} \]
Now substituting the value of the circumference:
\[ d = \frac{27}{\pi} \]
Using \( \pi \approx 3.14 \):
\[ d \approx \frac{27}{3.14} \approx 8.6 , \text{mm} \]
Thus, the diameter of the circle to the nearest tenth of a mm is 8.6 mm.