if(0.41 == (41*0.01)) is False and if(0.42 == (42*0.01)) is True .. Why?

In following script, I am getting 'false' for first condition and 'true' for second condition.

clc

clear all

if(0.41 == (41*0.01)) %First Condition

disp('true')

else

disp('false')

end

if(0.42 == (42*0.01)) %Second Condition

disp('true')

else

disp('false')

end

[Stephen23]

The effect of accumulated error with binary floating point numbers is very well documented:

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

[mathmach]

Thanks for these links :)

Now I got it and will read more on it.

Answer 1

[KSSV]

Read about comparing floating-point numbers.

tol = 10^-5 ; 
if(abs(0.41-(41*0.01)<=tol))       %First Condition
    disp('true')
else
    disp('false')
end

if(abs(0.42 - (42*0.01))<=tol )       %Second Condition
    disp('true')
else
    disp('false')
end

[mathmach]

Thanks :)