A United States dime coin is 1.35 mm thick. See related link.
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There is only one metric system. The relevant units, within that system would be millimetres.
A millimeter is closest in thickness to the thickness of a credit card or the edge of a dime.
A dime does not have weight in meters, as weight is typically measured in grams or ounces. However, if you are asking about the thickness of a dime, it is approximately 1.35 millimeters.
The thickness of the US dime is 1.35 millimeters. That's the same as 0.00135 meter, or 0.00000135 kilometer. You could use whichever of those you like, to remember the thickness of a dime or discuss it with other people. They're all correct. But the millimeter produces the most convenient number.
You would use the metric unit of grams to measure the mass of a dime. This would give you an accurate measurement of its weight.