The value of $0 . \overline{1}+0 . \overline{12}+0 . \overline{123}$ is
(A) $0 . \overline{343}$
(B) $0 . \overline{355}$
(C) $0.3 \overline{5}$
(D) $0 . \overline{355446}$
(E) $0 . \overline{355445}$
Since $0 . \overline{12}$ has a period of length 2 and $0 . \overline{123}$ has a period of length 3 , we must expand each of the three given decimals to six places:

$$
\begin{aligned}
& 0 . \overline{1}=0.111111 \ldots \\
& 0 . \overline{12}=0.121212 \ldots \\
& 0 . \overline{123}=0.123123 \ldots
\end{aligned}
$$

When we add these three numbers as decimals, we get

$$
0 . \overline{1}+0 . \overline{12}+0 . \overline{123}=0.355446 \ldots
$$

so the answer must be $0 . \overline{1}+0 . \overline{12}+0 . \overline{123}=0 . \overline{355446}$.

Answer: (D)