Weird-Confusing mistake in subtraction result!!!!

Hi everyone

I have a weird problem with a simple subtraction.

Here is my code. I define 'R' and 'a1 to a8':

R=194067676.886295
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
a1=19044444.410581;
a2=15000000.000000;
a3=1500000.000000;
a4=4000000;
a5=500000;
a6=32323232.475714; 
a7=120000000;
a8=1700000;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
sum=a1+a2+a3+a4+a5+a6+a7+a8
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
d=sum-R

As you can see from the result below, the value of 'R' and 'sum' is the same.

I expect the subtraction of 'R' and 'sum' which is 'd', becomes zero.

But as you can see, it isn't zero and I don't understand why is this happening.

result:

R =

     1.940676768862950e+08


sum =

     1.940676768862950e+08


d =

     2.980232238769531e-08
     

please help me with this problem.

I'm really confused.

Answer 1

[Stephen23]

"Weird-Confusing mistake"

Not weird, not a mistake, but perhaps confusing to the uninitiated.

"please help me with this problem."

Read about binary floating point numbers:

https://www.mathworks.com/matlabcentral/answers/57444-faq-why-is-0-3-0-2-0-1-not-equal-to-zero

https://www.mathworks.com/matlabcentral/answers/316889-why-two-equal-numbers-are-not-equal

http://www.mathworks.com/matlabcentral/answers/102419-how-do-i-determine-if-the-error-in-my-answer-is-the-result-of-round-off-error-or-a-bug

http://www.mathworks.com/matlabcentral/answers/140656-about-numerical-difficulty-of-equality-comparison-operation-between-two-double-real-numbers-in-matlab

This is worth reading as well:

https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html

http://faculty.tarleton.edu/agapie/documents/cs_343_arch/papers/1991_Goldberg_FloatingPoint.pdf

[shirin mhd]

I really appreciate your taking the time to explain the concept and share links. Im a novice coder and I'm learning a lot from here. Thank you for your help.