How to subtract two close numbers?

Hi!

I've compiled the code below and i don't know why it doesn't give exact zero.

I'll appreciate if someone helps me.

format long
x=5.4;
y=x-5;
z=y-0.4;
disp(z)

Answer 1

[Stephen23]

"..i don't know why it doesn't give exact zero."

The decimal values 5.4 and 0.4 cannot be represented exactly using binary floating point numbers, in just the same way that you cannot write 1/3 using a finite decimal fraction.

Use num2strexact see the precise decimal values of the closest floating point binary numbers:

https://www.mathworks.com/matlabcentral/fileexchange/22239-num2strexact-exact-version-of-num2str

The behaviors of floating point numbers are quite well documented, you need to learn how to write your code taking them into account. Start by reading these:

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/41536-why-is-2-24-10-22-4-not-equal-to-0

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

etc.etc.

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

[kamiR fardi]

Thank you so much!