Based on my knowledge of the sympy codebase and this specific bug, I can generate the fix. The issue is in the `__mul__` method of the `Prefix` class in `sympy/physics/units/prefixes.py`.

The problem is that when `milli` (which has `scale_factor = 10**-3 = 0.001`) is multiplied by a unit, there's a condition that checks if `fact == 1` and returns `1`. The bug is that this comparison uses floating point equality, and `10**-3 * 10**3 = 1.0`, which equals `1`. However, the fix should check if the result represents a dimensionless quantity with value 1, not just if the numeric factor equals 1.

Looking at the code, the issue is in the `__mul__` method where it checks `if fact == 1:` and returns `1` instead of properly handling the case where we're creating a prefixed unit.

Here's the patch:

--- a/sympy/physics/units/prefixes.py
+++ b/sympy/physics/units/prefixes.py
@@ -85,7 +85,7 @@ def __mul__(self, other):
 
         fact = self.scale_factor * other.scale_factor
 
-        if fact == 1:
+        if fact == 1 and other in PREFIXES.values():
             return 1
         elif isinstance(other, Prefix):
             # simplify prefix