R calculates small numbers, where the result should be zero

Hi
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
project.org] On Behalf Of Andrea Gonnermann
Sent: Tuesday, September 11, 2012 4:24 PM
To: r-help at r-project.org
Subject: [R] R calculates small numbers, where the result should be
zero

Hi all,

my problem is that R does wrong calculations, when the result should be
zero.
I have the following code:

 RD_Var1 <- ((0.1*(1-0.1))/100)+((0.2*(1-0.2))/100)
 RD_Var2 <- ((0.1*(1-0.1))/100)+((0.2*(1-0.2))/100)
 RD_1 <- 0.1-0.2
 RD_1
 RD_2 <- 0.1-0.2
 FEM_Eff_RD <-
((1/RD_Var1)*RD_1+(1/RD_Var2)*RD_2)/(1/RD_Var1+1/RD_Var2)
 Q_RD    <- 1/RD_Var1*((RD_1-FEM_Eff_RD)^2)+1/RD_Var2*((RD_2-
FEM_Eff_RD)^2)
 Q_RD
My result is:
1.540744e-31
When I put the calculated numbers directly into the last formula, I get
zero, which is the correct answer:
Q_RD    <- 1/0.0025*((-0.1--0.1)^2)+1/0.0025*((-0.1--0.1)^2)

Why does R calculate the other number instead of zero?
Because you are probably using computer. Some fractional decimal numbers cannot be expressed as binary finite precision numbers. You can round your result to get 0. BTW it is covered in FAQ 7.31 (I believe)

Regards
Petr
Thank you very much for your help!

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R calculates small numbers, where the result should be zero

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