Compare and Order: 55mm, 0.5cm, 0.007m, and 0.09dm from Smallest to Largest

Let's begin by converting each measurement to millimeters:

• $55$ mm is already in millimeters, so it stays at $55$ mm.
• $0.5$ cm = $0.5 \times 10$ mm = $5$ mm.
• $0.007$ m = $0.007 \times 1000$ mm = $7$ mm.
• $0.09$ dm = $0.09 \times 100$ mm = $9$ mm.

Now, comparing these converted lengths in millimeters:

• The smallest value is $5$ mm which corresponds to $0.5$ cm.
• The next smallest is $7$ mm which corresponds to $0.007$ m.
• The third is $9$ mm which corresponds to $0.09$ dm.
• The largest is $55$ mm which corresponds directly to $55$ mm.

Therefore, in ascending order, the lengths are:

$0.5$ cm
$0.007$ m
$0.09$ dm
$55$ mm