The metric unit for length closest to the thickness of a dime is the millimeter (mm).

Here's why:

* A dime is about 1.35 millimeters thick.

* While a centimeter (cm) is also a metric unit of length, it is equal to 10 millimeters. A dime is much thinner than 1 centimeter.

So, millimeters provide a more precise measurement for the thickness of a dime.