What’s The Mistake?

Find the mistake :

Step 1 : obviously true equality $ 2 = 200 c

Step 2 : square both sides ($ 2)² = (200c)²

Step 3 : doing calculations $ 4 = 40,000 c

Step 4 : converting cents into dollars $ 4 = $ 400

[from Number Puzzles by Sergiy Klymchuk]