Solution
= Solution
The ternary merges are $(.02,.03,.04)\mapsto.09$, then $(.04,.09,.14)\mapsto.27$, then $(.27,.28,.45)\mapsto1$. One code is
$$
x_1:0,\ x_2:1,\ x_3:20,\ x_4:21,\ x_5:220,\ x_6:221,\ x_7:222.
$$
Its expected length is
$$
\boxed{.45+.28+2(.14+.04)+3(.04+.03+.02)=1.36.}
$$