I am counting the number of nanorods contained in a sample (see picture below). The length scale is 1 µm. What units does the density have? Is it µm-2?
What units does the density have?
If you are considering volume density, the units of the density would be per cubic micrometer, or μm-3. Else if you are considering surface (areal) density, the units of the density would be per square micrometer, or μm-2.
This makes sense because the length scale is already defined at one micrometer, so the other two units will just be the multiplication of the length unit with itself.
If you're measuring - say - the weight of the nanorods instead, you would also need to prepend the appropriate weight (as defined by the scale).