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this is an inherent problem in using hex (or binary) float to represent decimal values: the representation will be inexact. You can even prove that one cannot represent 1/5 (and hence 1/10) exactly as a finite binary fraction.
There is, however, already a solution to this problem: use Decimal Floating Point (aka DFP). It is available via the FLOAT(DFP) compiler option
Or, if IBM does not want to impact existing functionality, can a new picture format be added that will instruct the compiler to do the conversion to packed as part of the display? F2P'(15)S9V.9999'.
PUT STRING(BUFFER) EDIT
('SHARES= ', FLTFLD1)
((1)A, F2P'(15)S9V.9999');
"... Can the accuracy of the picture display be improved for floating point variables?"
As you've already found out yourself, the ***only*** way to display floating point variables the way you want is to convert them into fixed point first.
Except for "a few" floating point values, most floating point variables ***cannot*** exactly be represented, not in IBM HEX format, nor in IEEE (754) floating point.
Any changes to the compiler, unless a new RULES() option is introduced would break numerous other programs - you may want to see 0.5700, whereas Tom, Dick or Harry absolutely require 0.5699...