Suppose I want to express $3h$ in units of $\hbar$ (where $h$ and $\hbar$ are the Planck constant and reduced Planck constant, respectively). By definition, $h = 2\pi\hbar$, but when I attempt this conversion using Mathematica's built-in unit functions,

UnitConvert[Quantity[3, "PlanckConstant"], "ReducedPlanckConstant"]
    (* => 18.84956 ℏ *)

I obtain a non-exact (floating-point) result.

In general, I've observed that whenever I want to convert between two units for which there is an irrational (but exactly known) conversion factor (e.g. a multiple of $\pi^n$), Mathematica fails to give the exact result. Is there a way to fix this?

UnitConvert[Quantity[3, "PlanckConstant"], "ReducedPlanckConstant"] /.
  x_?NumericQ :> RootApproximant[x/Pi]*Pi

Quantity[6*Pi, "ReducedPlanckConstant"]


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