numerical oddity with decimal multiplication

Running R2022b, I noticed the following:

58*0.1-5.8

ans =

   8.8818e-16

However,

58/(1/.1)-5.8

ans =

     0

Why is that, and how can it be avoided? It messes up subsequent equality operations.

Some further testing shows that

58*0.1-5.8-4*eps

ans =

     0

57*0.1-5.7

ans =

     0

59*0.1-5.9

ans =

     0

and in fact it's 0 for most numbers´I randomly tested, however

28*0.1-2.8-2*eps

ans =

     0

Thanks in advance to anyone able and willing to clarify :)

[Stephen23]

"Why is that"

Because binary floating point numbers have finite precision, which has the effect that arithmetic operations on them necessarily accumulate floating point error. You (the programmer) need to understand that, and take that into account in your algorithms.

"and how can it be avoided?"

It can't be avoided (if you want to store data using 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

Answer 1

[the cyclist]

Possibly the most "popular" question on this forum. Read the Accuracy of Floating-Point Data section of the Floating-Point Numbers documentation.

(You will also get many other answers here, but they will all boil down to that same information.)