Precision can be explicitely set as second argument for GMP::F.new().

If there is no explicit precision, highest precision of all GMP::F arguments is used.
That doesn't ensure that result will be exact. For details, consult any
paper about floating point arithmetics.

Default precision can be explicitely set by passing 0 to GMP::F.new().
In particular, you can set precision of copy of GMP::F object by:
    new_obj = GMP::F.new(old_obj, 0)

Precision argument, and default_precision will be rounded up to whatever
GMP thinks is appropriate.