1) How many digits does the number $2^{3} \cdot 5^{4} \cdot 10^{5}$ have?
(A) Six,
(B) Seven,
(C) Eight,
(D) Nine,
(E) None of the above.
1. The answer is $(\mathbf{D})$. Observe that $2^{3} \cdot 5^{4} \cdot 10^{5}=2^{3} \cdot 5^{3} \cdot 5 \cdot 10^{5}=10^{3} \cdot 5 \cdot 10^{5}=5 \cdot 10^{8}$. Therefore, the number we are considering is between $10^{8}$ and $10^{9}$, excluding the endpoints; hence it has 9 digits.