A document with 300px height and width with a ppi of 300 is 4.17in?

I'm totally new to Illustrator and need to make a document that is going to be placed in a magazine ad (it's a free placement, hence why I'm just trying to do it myself). I can get around in PhotoShop, but Illustrator is confusing to me. The ad dimensions are supposed to be:
2.33" w x 7.5" h
700 x 2250 pixels
When I create a new Illustrator document, leaving the Raster Effects setting in the Advanced section at 300ppi, if I change the Units setting to pixels, put in 300 for width and height, then change the Units back to Inches, it says the width and height are 4.17 in.
Why is that?
I'm so confused :-/

Print work doesn't use pixels.
Set the document to 2.33" x 7.5"
Click the "Advanced" option in the New Document Window and ensure that the Color Mode is CMYK and then Raster Effects is set to High (300ppi) and you are done.
You can't think in terms of pixels for print work.
Illustrator, being a vector application, is resolution indepenedent. This means it doesn't use pixels at all unless you place a raster image into Illustrator or use a raster effect within Illustrator. the Raster Effect setting ensures any raster elements created within Illustrator are created at the correct resolution.

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