What is the numeric precision of Network Difficulty?

My understanding is that Difficulty (aka Network Difficulty) is an approximate representation of the Target, a 256-bit number which is hard to reason about or work with in human-readable Decimal format.

The Bitcoin wiki defines Difficulty as: difficulty = difficulty_1_target / current_target, where difficulty_1_target was the Target during the first Difficulty Epoch (the first 2016 blocks).

Is this definition of Difficulty correct? If yes, is it accurate to think about Difficulty as a type of proportion or ratio? And if it is a floating point number, what is its precision?

I don't often work with hexadecimal or 256-bit numbers, so I am confused where the "approximation" piece comes in, making Difficulty values easier to work with than the Target. Is Difficulty rounded after some decimal place?

Lastly, could someone please confirm the formula used to compare a hash against the Target, to see if it mines a valid block? For more practical use, how would you represent this formula using Difficulty instead of the Target?

Thank you



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