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Are there any HP calculators more advanced than the 32SII that support fractions (e.g., entering and displaying 1/3 rather than 0.3333)?

Yes, most of hp calcs produced after the 32SII do show up numbers as fractions if requested so.

>Are there any HP calculators more advanced than the 32SII >that support fractions (e.g., entering and displaying 1/3 >rather than 0.3333)?

Actually the HP32SII does allow to enter fractions and
also allows to convert a decimal number to a fractional format.

As an example, to enter 4 5/16 just type in
4[.]5[.]16
To enter, let's say 3/5, it's possible to type in
either 0[.]3[.]5 or 3[.][.]5

In order to revert a decimal number to a fractional
format use [green shift] [FDISP] to toggle between decimal
and fractional display mode.
As an example, with 4.3125 in the X register,
[green shift] [FDISP] will displays it as 4 5/16.
The manual explains this better. :-)

Other than that, with the HP48 a fraction can be entered
as an algebraic object: as an example, 5/16 can be entered as '5/16'.
To convert a decimal number into a fraction, there is the built-in funtion ->Q, whose accuracy depends upon the
format of the display.

The HP30S works with fractions, and is easy to convert from, say, 1.25 to 5/4 to 1 1/4, etc. with it. However, as the 30S is nonprogrammable and not RPN, I would not say it is more advanced than the 32Sii.