khwilson opened a new pull request, #44120:
URL: https://github.com/apache/arrow/pull/44120

   ### Rationale for this change
   
   UUID extension types were made canonical in #41299 and are getting native 
support in C++ and Python in #37298. As such, it makes sense to provide an 
alternative user-defined extension type as an example that is unlikely to 
become a canonical extension type anytime soon.
   
   After discussion in #43809, we determined a `RationalType` would make sense.
   
   Please note that this is a redo of #43849 as I made a blunder and 
accidentally pushed a branch that was in a wonky state.
   
   ### What changes are included in this PR?
   
   A change in several doc locations which reference a `UuidType` extension 
type have been changed to a `RationalType`.
   
   For consistency, this PR also changes single quotes (`''`) to double quotes 
(`""`) throughout the Python examples that it modifies.
   
   Also, seemingly unrelated to this change, some doctests began failing as 
numpy changed the `repr` of `float16`'s between 1.x and 2.x. We have updated 
the failing doctest so that it supports both styles.
   
   ### Are these changes tested?
   
   These are documentation changes and `archery docker run conda-python-docs` 
succeeds locally.
   
   ### Are there any user-facing changes?
   
   No.
   
   cc @ianmcook @rok 
   * GitHub Issue: #43809
   


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