Molecules in a teaspoon? Teaspoons in the ocean?

So back in college, I had a physics professor ask the class "Is there more molecules of water in a teaspoon, or more teaspoons of water in the oceans?" I initially thought there were more molecules of water in a teaspoon, but I didn't know for certain. Today, I did the calculations. Let’s start with the teaspoon.

1 Teaspoon of water is ~5cm³
The molecular weight of water is 2*(1.00794) + 15.9994 == 18.01528 g/mole

Water is pretty convenient in that it weighs 1 gram per cm³

5 g/18.01528 g/mol == .278 moles/teaspoon

6.022e23 * .278 == 1.67e23 molecules of water per teaspoon


Next, the world's oceans.

Surface area of Earth is ~500000000km²
Roughly 70% of the earth is covered in water.
The earth's average ocean depth is 4 km
1 km³ is 1e15 cm³

500000000*.7*4*1e15 == 1.4e24 cm³ of water in the ocean

Divide that number by the size of a teaspoon, and you get
1.4e24/5 == 2.8e23 teaspoons of water in the ocean

And we have our conclusion that there are in fact more teaspoons of water in the oceans, than there are molecules of water in a teaspoon. Long story short, I was wrong.