Converting and Ordering Length Units: 0.03m, 5cm, 25mm, and 0.001dm

To solve this problem, we need to convert all the given lengths to a common unit of measurement, here we'll use meters.

First, let's convert each measurement to meters:

• $0.03$ m is already in meters.
• $5$ cm: Since $1 \text{ cm} = 0.01 \text{ m}$, then $5 \text{ cm} = 5 \times 0.01 \text{ m} = 0.05 \text{ m}$.
• $25$ mm: Since $1 \text{ mm} = 0.001 \text{ m}$, then $25 \text{ mm} = 25 \times 0.001 \text{ m} = 0.025 \text{ m}$.
• $0.001$ dm: Since $1 \text{ dm} = 0.1 \text{ m}$, then $0.001 \text{ dm} = 0.001 \times 0.1 \text{ m} = 0.0001 \text{ m}$.

Next, we compare the values we have in meters:

• $0.0001$ m (from $0.001$ dm)
• $0.025$ m (from $25$ mm)
• $0.03$ m
• $0.05$ m (from $5$ cm)

Thus, ordering from smallest to largest is: $0.001$ dm, $25$ mm, $0.03$ m, $5$ cm.

Therefore, the correct order from smallest to largest is:

$0.001$ dm
$25$ mm
$0.03$ m
$5$ cm