There are bits to a Trit. This can be interpreted a few different ways:

If you multiply the number of messages you might want to send by 3, then the cost of encoding the message will go up by 1.58 bits on average. See Marginal_message_cost for more on this interpretation.

If you pack $n$ of independent and equally likely 3-messages together into one giant $3^{n}$ message, then the cost (in bits) per individual 3-message drops as $n$ grows, ultimately converging to ${log}_{2} (3)$ bits per 3-message as $n$ gets very large. For more on this, see Average_message_cost and the GalCom example of encoding trits using bits.

The infinite expansion of ${log}_{2} (3) = 1.58496250072 \dots$ tells us not just how many bits it takes to send one 3-message $(\approx ⌈ 1.585 ⌉ = 2)$ but also how long it takes to send any number of 3-messages put together. For example, it costs 2 bits to send one 3-message; 16 bits to send 10; 159 bits to send 1000; 1585 to send 10,000; 15850 to send 100,000; 158497 to send 1,000,000; and so on. For more on this interpretation, see the "series of ceilings" interpretation of logarithms.