Re: Adding two numbers of high precision results in a number of low precision??

*To*: mathgroup at smc.vnet.net*Subject*: [mg56981] Re: Adding two numbers of high precision results in a number of low precision??*From*: "Peltio" <peltio at trilight.zone>*Date*: Thu, 12 May 2005 02:32:14 -0400 (EDT)*References*: <d5mv2v$dv0$1@smc.vnet.net>*Reply-to*: "Peltio" <peltioNOSPAM at despammed.com.invalid>*Sender*: owner-wri-mathgroup at wolfram.com

"Kees van Schaik" wrote >> Precisie bTemp[3,0,0] = 389.685 >> Precisie Q[3,1] = 390.729 >> Precisie bTemp[3,0,1] =53.8232 > > >Now the first one makes sense, but the last one, how is it possible that >if I add two numbers of precision ca. 390 I get something of precision >53 back? Cancellation of significant digits? *If* the two numbers have different signs, this could happen. For example: a=+2.1234567895 b=-2.1234567891 a+b=0.4*10^-10 The first two numbers have a precision of 11 digits. Their sum has a precision of 1. cheers, Peltio PS To see this in Mathematica, you should experiment with numbers with more then 16 digits, lest not to fall in the machine precision Maelstrom. a = +2.3333333333333333335; b = -2.333333333333331245; Precision[a] Precision[b] Precision[a + b]