Infinite loop when decimals are added

I am making a simple program to calculate the number of times a decimal number has to be multiplied (by positive integers) so that the decimal part (mod1) will = 0.

Example of the code:

%Decimal
ro=0.5854;
n=1;
while mod(ro*n,1)~=0
    n=n+1;    
end
n

In this case the answer is 5000.

I want to be able to change the last digit of the decimal point. But I am having a problem when I make a small change in the program. I get an infinite loop. The changed program is shown below:

%Decimal
ro=0.585+0.0004;
n=1;
while mod(ro*n,1)~=0
    n=n+1;    
end
n

I can't understand why I get an infinite loop with this small change - the value of ro changed acordingly but I get an infinite "while" loop. Please explain.

Answer 1

[Stephen23]

"Please explain"

Different accumulated floating point error combined with an algorithm that does not take into account the behavior of binary floating point numbers. Also note that the values are not the same:

fprintf('%.30f\n', 0.5854, 0.585+0.0004)

0.585400000000000031441516057384
0.585399999999999920419213594869

Read more 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

[Leonel Sternberg]

Thanks ..This helps