Ordering Length Measurements: 0.2m, 35mm, 15cm, and 0.05dm Comparison

To order the given lengths from smallest to largest, we need to convert each measurement into meters:

• $35 \text{ mm}$: Convert using $35 \text{ mm} \times 0.001 = 0.035 \text{ m}$.
• $15 \text{ cm}$: Convert using $15 \text{ cm} \times 0.01 = 0.15 \text{ m}$.
• $0.05 \text{ dm}$: Convert using $0.05 \text{ dm} \times 0.1 = 0.005 \text{ m}$.
• $0.2 \text{ m}$ is already in meters.

After conversion, we have:

• $0.035 \text{ m}$ from 35 mm
• $0.15 \text{ m}$ from 15 cm
• $0.005 \text{ m}$ from 0.05 dm
• $0.2 \text{ m}$.

Next, arrange these values from smallest to largest:

• $0.005 \text{ m}$ from $0.05 \text{ dm}$
• $0.035 \text{ m}$ from $35 \text{ mm}$
• $0.15 \text{ m}$ from $15 \text{ cm}$
• $0.2 \text{ m}$ from $0.2 \text{ m}$.

The ordering from smallest to largest is $0.05 \text{ dm}$, $35 \text{ mm}$, $15 \text{ cm}$, $0.2 \text{ m}$.

Therefore, the correct order is choice 1:

$0.05$ dm
$35$ mm
$15$ cm
$0.2$ m