Compare and Order: 0.04m, 8cm, 50mm, and 0.2dm in Metric Units

To solve this problem, we'll follow these steps:

• Step 1: Convert each length to meters for a fair comparison.
• Step 2: Order the lengths from smallest to largest.

Now, let's work through each step:

Step 1: Convert all measurements to meters.

• $0.04 \, \text{m}$ is already in meters.
• $8 \, \text{cm} = \frac{8}{100} \, \text{m} = 0.08 \, \text{m}$.
• $50 \, \text{mm} = \frac{50}{1000} \, \text{m} = 0.05 \, \text{m}$.
• $0.2 \, \text{dm} = \frac{0.2}{10} \, \text{m} = 0.02 \, \text{m}$.

Step 2: Order the lengths from smallest to largest based on the meter conversions:

• $0.02 \, \text{m}$ (which is $0.2 \, \text{dm}$)
• $0.04 \, \text{m}$
• $0.05 \, \text{m}$ (which is $50 \, \text{mm}$)
• $0.08 \, \text{m}$ (which is $8 \, \text{cm}$)

Therefore, the order from smallest to largest is:

$0.2 \, \text{dm} < 0.04 \, \text{m} < 50 \, \text{mm} < 8 \, \text{cm}$.