cosmology - Dumbed-down explanation how scientists know the number of atoms in the universe?

It is often quoted that the number of atoms in the universe is 10$^{70}$ or 10$^{80}$.

How do scientists determine this number?

And how accurate is it (how strong is the supporting evidences for it)?

Is it more likely (logically >50% chance) that the numbers are right, or is it more likely that the numbers are wrong?