Order-of-magnitude count of fish in the sea

Estimate how many fish live in the world's oceans.

On the order of a trillion or a few trillion. The ocean covers about $3.6\times10^8\ \text{km}^2$, but most fish live in productive coastal and upper-ocean waters; assume about $10\%$ is productive at perhaps $10^5$ fish per square kilometre (counted through the water column) and the rest much sparser, giving roughly $10^{12}$–$10^{13}$. Scientific estimates are around $3.5$ trillion; the logic and the uncertainty range matter more than the figure.