A square with a side length of $1 \mathrm{~m}$ was cut, with cuts parallel to its sides, into small squares with a side length of $1 \mathrm{~mm}$. By placing these small squares side by side, without overlapping, a rectangle with a width of $1 \mathrm{~mm}$ was formed. What is the length of this rectangle?
Solution 1: Converting meters to millimeters, we have $1 \mathrm{~m}=1000 \mathrm{~mm}$. Thus, the square is divided into $1000 \times 1000=10^{6}$ small squares, each with a side of $1 \mathrm{~mm}$. Placing all $10^{6}$ small squares side by side, we will have a rectangle with a length of

$$
\underbrace{1+1+\cdots+1}_{10^{6} \text { terms }}=10^{6} \times 1=10^{6} \mathrm{~mm}=1 \mathrm{~km}
$$

Solution 2: The square has an area equal to $1 \mathrm{~m}^{2}=10^{6} \mathrm{~mm}^{2}$. The area $\Delta$ of the rectangle is the same as that of the square. Since the width of the rectangle is $\ell=1 \mathrm{~mm}$, it follows that the length $c$ of the rectangle, in millimeters, is

$$
c=\frac{\Delta}{\ell}=\frac{10^{6}}{1}=10^{6} \mathrm{~mm}
$$