I have a CMYK document, and it has a linked image in it, with an intentionally chosen profile, with some specific colors set for the background, and these have to be the part of the background, because of blending modes used.
Now I need to grab those colors form the clear parts of the background to quickly transfer them into vector part of the design. But when I try — Ai lies about values.

Instead of
70-15-0-0
0-35-85-0
0-95-20-0
I get
69.8-14.9-0-0
0-34.9-85.1-0
0-94.9-20-0

Not much, right? Just 0.2%, why are you mad?
But these would be enough to break Select Same Fill later, duplicate swatches if added next to existing ones in other documents, drop my trust level for the tool and force me cleaning this mess in the time I need I can’t spend. Sure, there are methods to help with this, but it’s not MY error. It’s Ai’s lie.

...later Ton Frederiks suggested it’s Photoshop that is rounding numbers.
To quote: if the placed file gets rasterized, it gives the fractions in Illustrator. But if the file gets exported from Illustrator as .tif, Photoshop will show the same rounded numbers it started with. Photoshop will not allow fractions and force round numbers when we try to enter percentages like 69,8%. CMYK values go from 0-100 while image values have a range from 0-255.

Indeed, I tried to rasterize a rectangle with fractions in CMYK color (55.69) and opened the image in Photoshop — and got integers, 56...
But then I mix the very same color in Ps, making integers manually, fill half of the image with this new color and try to pick colors from this image in Ai: Ai still picks the original 55.69 from the original half of the image... and 56.08 from the half I flooded with Ps’s 56!
And Ps SEES them as different color when Color Picker is used, displaying different Lab, RGB, HSB values, but CMYK stays the same, rounded.

In my experiment below I did a similar thing: created these in Ai first (but no fractions), rasterized it, used to make a composition and placed back into Ai.
Double conversion and forcing integers (visually) would explain it.

So Ai is rather precise... but the irritation stays.
Now the question would be — what to do with the uncomfortable truth? 'Fighting ignorance' is my favorite choice, but...

I don’t have a clear solution to this — and I invite others to a discussion — but perhaps the Eyedropper can get an option to Emulate Photoshop Eyedropper (round CMYK values)?