Numerical accuracy/precision - this is a bug or a feature?

*To*: mathgroup at smc.vnet.net*Subject*: [mg119992] Numerical accuracy/precision - this is a bug or a feature?*From*: "slawek" <slawek at host.pl>*Date*: Mon, 4 Jul 2011 06:45:07 -0400 (EDT)

Let Mathematica (6.x, 7.x) compute quite a simple product In[1]:= N[N[2.0, 20] * N[Sqrt[2] , 20], 20] Out[1]= 2.82843 This is a bug. Why? Now we analyze it in details: 1. N[2.0,20] should give 2 with accuracy/precision/whatsever about 20 decimal digits, i.e. 2.00000000000000000000 2. Sqrt[2] should give... Sqrt[2] 3. N[Sqrt[2]] should give 1.4142135623730950488 (this is copy-paste from Mathematica output to N[Sqrt[2]] ) 4. The product 2.00000000000000000000 * 1.4142135623730950488 is 2.8284271247461900976 (again copy-paste) 5. BUT THE RESULT OF N[2.0, 20] * N[Sqrt[2] , 20] "truncated to 20 digits" is Out[1]= 2.82843 Where are missing digits?! slawek