1. How many digits does the number $\left[1.125 \cdot\left(10^{9}\right)^{5}\right]:\left[\frac{3}{32} \cdot 10^{-4}\right]$ have?
1. Simplify the given expression:

$$
\begin{array}{ll}
{\left[1.125 \cdot\left(10^{9}\right)^{5}\right]:\left[\frac{3}{32} \cdot 10^{-4}\right]=\left[\frac{1125}{1000} \cdot 10^{45}\right]:\left[\frac{3}{32} \cdot 10^{-4}\right]=} & 1 \text{ POINT} \\
=\left(\frac{9}{8}: \frac{3}{32}\right) \cdot\left(10^{45}: 10^{-4}\right)= & 1 \text{ POINT} \\
=\left(\frac{9}{8} \cdot \frac{32}{3}\right) \cdot\left(10^{45-(-4)}\right)= & 1 \text{ POINT} \\
=12 \cdot 10^{49} & 1 \text{ POINT}
\end{array}
$$

This number, in its notation, has the first two digits as 1 and 2, followed by 49 zeros, making the total number of digits 51.