This grabs the length factor (1 cm = 10 mm) and stops. But area is 2-D, so a single length factor is never enough. Wrong answer.
The truth (area factor)
Used the area factor (10²)
5 cm² × 100 = …
500 mm²
1 cm² is a 10 mm by 10 mm square = 100 mm². So you multiply by 10² = 100, not by 10.
Convert:
Both columns show the same square. The mistake is using the length factor (×10 for cm→mm, ×100 for m→cm). Area needs the factor squared: ×10² = 100 for cm²→mm², and ×100² = 10 000 for m²→cm². Watch the gap between the two answers explode.