Order Length Units: Converting 2cm, 0.4dm, 30mm, and 0.01m

To order the given lengths from smallest to largest, we first convert all measurements to a common unit, such as centimeters:

• $2$ cm is already in centimeters.
• $0.4$ dm: Using the conversion $1$ dm = $10$ cm, $0.4$ dm = $0.4 \times 10 = 4$ cm.
• $30$ mm: Using the conversion $1$ mm = $0.1$ cm, $30$ mm = $30 \times 0.1 = 3$ cm.
• $0.01$ m: Using the conversion $1$ m = $100$ cm, $0.01$ m = $0.01 \times 100 = 1$ cm.

Now, we can arrange the lengths in ascending order by their converted measurements:

• $0.01$ m = $1$ cm
• $2$ cm = $2$ cm
• $30$ mm = $3$ cm
• $0.4$ dm = $4$ cm

Therefore, the correct order from smallest to largest is:

$0.01$ m
$2$ cm
$30$ mm
$0.4$ dm