Be careful about te floating thing- if you check eggs from the store, you will find that a lot of them will float a little, eggs generally don't sit on the bottom of a basin of water unless they're REALLY freshly laid.
I float-test eggs which I'm not sure about (if I find a nest, for example, that they could have been laying in for weeks without me knowing) and any eggs which float high in the water, are the ones I'm suspicious of.
I remember being taught how to put eggs on to boil and my mother saying, "Just cover the eggs with water," and me saying, "But the eggs are floating, they won't cover, they're rising up with the water."
And these were eggs fresh from the shop. The thing is, they were only floating to barely break the surface of the water. That's not really "floating" as in rotten eggs.
Writing the date on the egg is a good way to know how old they are. I add a question mark if I don't know how long the egg was there before I found it. Then when I'm using them, I brak each egg into a cup separately, so if one IS off, it won't spoil everything else.
After years of having our own eggs, and also having some eggs of very suspect age and condition, I've still had very few "rotten egg in the house" incidents.
And a note on condition - if you find an egg which has been sitting in manure for an unknown period of time, but at least a number of days or a week, especially if there has been a lot of moisture and a lot of hot weather, the egg may not float high but could well be off. You won't be in any doubt. Trust me.
So always clean your eggs if they're grotty.
Marg