Why do I get false results when using equal relational operation for the logical operation?

I would like to get true when I use equal rational operation in a code including if condition. But I got false for the equal rational operation like as the below example. For example:

   a = 0.2;
   b = zeros(3,1);   
   if 12*a == 2.4   
         b(1) = 1; 
   end   
   if 14*a == 2.8 
      b(2) = 2; 
   end 
    if 17*a == 3.4  
     b(3) = 3; 
  end  
>> b  b =       0      0      0

Answer 1

[Anish]

If you look carefully at the definition of fundamental arithmetic operations like addition and multiplication, you soon encounter the mathematical abstraction known as the real numbers. But actual computation with real numbers is not very practical because it involves limits and infinities. So you need to avoid to using the result of multiplying floating points for the equal (==) operation because the result of multiplying floating points make the round off error.

Here is the link for the reference of floating points including IEEE Standard unifies arithmetic model:

http://www.mathworks.nl/company/newsletters/news_notes/pdf/Fall96Cleve.pdf

As workarounds for this issue, use the integer for the variable 'a=2' instead of using floating points 'a=0.2' or rewrite your code like as below:

if (abs(a*12 - 2.4) < eps*10)

Answer 2

[Walter Roberson]

See also FAQ #6.1