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In the SI - the current metric system - that would be the kilogram. In older metric systems, the gram has been used as the unit of mass.
The liter is a metric unit of capacity (volume). The meter is the fundamental unit of length in the metric system.
No. "Metric" refers to a system of measurement - of mass, length, volume etc. Tonne is a unit for measuring mass.
The kilogram is the official unit of mass.
Carat IS a metric unit of mass