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2013-02-11 10:09:03 +0200	marked best answer	Arbitrary precision with power function You have lost precision in the exponent. Use this instead: `sage: RealField(1000)(3*RealField(1000)(2.72)) 19.8504251527275236501169613591809343996536832818298893731367232890539239539110192928936229752670609756876526611313601647375707220812753965333394338326864664393162650498858490630921586590646536288686549507904739021525557865246462265058167658909360187069317683688989045025859261795668964872237430699403` EDIT: In general, I think you need to ensure that you don't* try to get higher precision after your computations. Rather, start with the higher precision from the very beginning.
2013-02-11 10:09:03 +0200	received badge	● Scholar (source)
2013-02-11 10:08:48 +0200	commented answer	Arbitrary precision with power function I understand. Thank you! It's work. Also example for maxima: fpprec:5000; bfloat(3.0b0 ^ 2.72b0); Example for GP/PARI: \p 1000 3^2.72
2013-02-08 23:46:14 +0200	received badge	● Supporter (source)
2013-02-08 21:53:21 +0200	asked a question	Arbitrary precision with power function Hello! Sorry for my english. Why in Sage 5.6 numerical_approx((32.72), digits=200) gives 19.850425152727527944307439611293375492095947265625000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000000000000000 and RealField(1000)(32.72) gives 19.850425152727527944307439611293375492095947265625000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000000000000000000000000000000\ 0000000000000 ? After digit 5 zero, zero, zero. How to get more digits in Sage?