1997 AHSME Problem 29

Call a positive real number special if it has a decimal representation that consists entirely of digits 0 and 7. For example, \frac{700}{99}= 7.\overline{07}= 7.070707\cdots and 77.007 are special numbers. What is the smallest n such that 1 can be written as a sum of n special numbers?

\begin{array}{l} \textbf{(A)}\ 7\qquad\textbf{(B)}\ 8\qquad\textbf{(C)}\ 9\qquad\textbf{(D)}\ 10\qquad\\ \textbf{(E)}\ \text{The number 1 cannot be represented as a sum of finitely many special numbers.} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.