Having the mole as an SI base unit is kind of like having "the dozen" (12) as an SI base unit
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Avogadro. The smouldering talent that wowed Stewart Granger in Bhowani Junction
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It is weird, but incredibly useful. The weirder thing is THE Kilogram, because the definition requires a set of metal cylinders stored in jars across the world The best alternative we have is a crystal ball made by a 70 year old, using his hands and that number. Not even kidding
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There is a better alternative. Look up the watt balance, aka Kibble balance.
End of conversation
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Not particularly. It's a scaling factor; the fact that these are always dimensionless is just an artifact of what we consider "dimensions" to be.
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