B4. We define the number $A$ as the digit 4 followed by the digit combination 84 repeated 2024 times, and the number $B$ as the digit combination 84 repeated 2024 times followed by a 7. To illustrate, we have

$$
A=4 \underbrace{84 \ldots 84}_{4048 \text { digits }} \text { and } B=\underbrace{84 \ldots 84}_{4048 \text { digits }} 7 \text {. }
$$

Simplify the fraction $\frac{A}{B}$ as much as possible.
B4. We first look at some smaller cases with only 0, 1, or 2 occurrences of the digit combination 84:

$$
\frac{4}{7}=\frac{4}{7}, \quad \frac{484}{847}=\frac{4 \cdot 121}{7 \cdot 121}=\frac{4}{7}, \quad \frac{48484}{84847}=\frac{4 \cdot 12121}{7 \cdot 12121}=\frac{4}{7}
$$

For our very large number $A$, we immediately see that $A=484 \ldots 84=4 \cdot 121 \ldots 21$, while we can view $B$ as $7 \cdot 121 \ldots 21$. This leads to $\frac{A}{B}=\frac{4}{7}$.