Here why are conversions like that

A conversion factor is a ratio of two equivalent quantities expressed in different units. Since the numerator and denominator represent the same amount, the conversion factor is essentially equal to 1.
For example, we know that $1 \text{ m}$ is the same length as $1000 \text{ mm}$.
So, we can form two conversion factors:

$$\frac{1000 \text{ mm}}{1 \text{ m}} \quad \text{or} \quad \frac{1 \text{ m}}{1000 \text{ mm}}$$

Both of these fractions are equal to 1.

To convert a quantity, you multiply it by the appropriate conversion factor. The goal is to choose the factor that allows the original unit to cancel out, leaving the desired unit.

Let's use the example of converting $5 \text{ m}$ to millimeters:

$$5 \text{ m} \times \frac{1000 \text{ mm}}{1 \text{ m}}$$

Here, the unit 'm' in the numerator of $5 \text{ m}$ cancels with the unit 'm' in the denominator of the conversion factor:

$$5 \cancel{\text{ m}} \times \frac{1000 \text{ mm}}{1 \cancel{\text{ m}}} = 5 \times 1000 \text{ mm} = 5000 \text{ mm}$$

If we had chosen the other conversion factor, the units would not cancel correctly:

$$5 \text{ m} \times \frac{1 \text{ m}}{1000 \text{ mm}} = \frac{5 \text{ m}^2}{1000 \text{ mm}}$$

This result is not in millimeters, indicating the wrong conversion factor was used.

The structure of conversions ensures that you are multiplying by 1 (so the value doesn't change) while simultaneously changing the units by cancelling them out.