Consider this:

sage: R100=RealField(100)
sage: x= R100(8/3)
sage: R=RealField()
sage: R(x)
2.66666666666667
sage: RDF(x)
2.66666666667

The documentation says that in RealField() and RDF, numbers are represented with the same precision of 53 bits.
So, R(x) and RDF(x) should give the same result... I think..

Yours
t.d.

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