The boiling and melting points of water aren’t that precise, because it varies with armospheric pressure. While the original definition of the Celsius referred to those, the current definition is actually defined based on the Triple Point of water, which is a more reproducible standard, and absolute zero, which is a universal constant. (Actually, the current current definition is to do with the Boltzmann constant, but that’s unimportant for our purposes)
Basically, the reason why there’s only two decimal places of precision is because that’s the definition of the Celsius.
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