To find the long-run relative frequency of tails, we first need to determine how many tails were observed. Since the coin was tossed 300 times and heads were observed 180 times, we can calculate the number of tails as follows:
\[ \text{Number of tails} = \text{Total tosses} - \text{Number of heads} = 300 - 180 = 120 \]
Next, we can find the long-run relative frequency of tails by dividing the number of tails by the total number of tosses:
\[ \text{Long-run relative frequency of tails} = \frac{\text{Number of tails}}{\text{Total tosses}} = \frac{120}{300} \]
Calculating this gives:
\[ \frac{120}{300} = 0.4 \]
Therefore, the long-run relative frequency of tails is \( \boxed{0.4} \).