Compare Units: Ordering 30mm, 0.09dm, 6cm, and 0.04m from Smallest to Largest

To solve this problem, we will convert each measurement to millimeters so that we can easily compare their sizes:

• Convert $0.09 \, \text{dm}$ to mm: $0.09 \, \text{dm} = 0.09 \times 100 \, \text{mm} = 9 \, \text{mm}$
• Convert $6 \, \text{cm}$ to mm: $6 \, \text{cm} = 6 \times 10 \, \text{mm} = 60 \, \text{mm}$
• Convert $0.04 \, \text{m}$ to mm: $0.04 \, \text{m} = 0.04 \times 1000 \, \text{mm} = 40 \, \text{mm}$

Now, compare the lengths in millimeters:

• $9 \, \text{mm}$ (originally $0.09 \, \text{dm}$)
• $30 \, \text{mm}$ (originally $30 \, \text{mm}$)
• $40 \, \text{mm}$ (originally $0.04 \, \text{m}$)
• $60 \, \text{mm}$ (originally $6 \, \text{cm}$)

The order from smallest to largest is:

$0.09 \, \text{dm}$, $30 \, \text{mm}$, $0.04 \, \text{m}$, $6 \, \text{cm}$