Dimensions changes when placing image in Illustrator

I had a problem while placing an image created in photoshop into illustrator, dimensions of the image was changed in Illustrator (shorter in hight and longer in width). My image size in Photoshop is 30.6 cm x 6 cm, Resolution: 300 pixels/inch, it changed in illustrator to 30.4969 cm x 6.0029 cm.
After few tests, I found out that if I change image resolution from pixels/inch to pixels/cm, resolution hence will convert from 300ppi to 118.11. Here I just rounded resolution to 120ppc, only then this image will keep its dimensions in illustrator as 30.6 cm x 6 cm without any change when I drag it or place it in Ai again!
Apparently keeping resolution as rounded figures in pixels/cm will fix this issue… any one had this problem or had solved it in a different way?

I think this is down to specifiying metric dimensions in an imperial resolution, coupled with the fact that there's no such thing as a fraction of a pixel.
300dpi equals 118.1102362 pixels per cm. Therefore, 6cm equals 708.6614173 pixels. Because you can only have whole pixels, Photoshop rounds this up to 709 pixels. 709 divided by 118.1102362 equals 6.002866668 which accounts for the discrepancy that you're seeing.
As you've discovered, the only way around this is to use a metric resolution that your chosen dimension fits in exact pixels.

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