How to make AI document display same physical size as mobile screen?

I know this seems like a bush-league sort of question, but I can't find the answer.
I'm designing some screens for an retina display iPad and I just want the illustrator document on my 27" thunderbold monitor (at 109 ppi) to have the same physical dimensions as the physical iPad screen (7.75" x 5.81").  Maybe its so obvious that no one talks about how to do it.  I do feel a little embarassed that I haven't figured this out.
Regardless of whenther I enter the doucment dimensions in inches or in pixels the resulting document is never the same pysicial size as the iPad's screen.  And since Illustrator deals in vectors it doesn't have any notion of PPI that I can use to bring inches and pixels into alignement so that what I see on my monitor is the same physical size as what's in the iPad.
All i want is the AI document displayed on my monitor to be the exact same size as my iPad's screen.  Can anyone help?

Photoshop has a "Screen Resolution" feature in its Settings which allows you to enter your screen resolution of 109 and this will display the physical size of images when you choose Print Size from the View menu. It simply will display the image at the appropriate zoom level for you. Unfortunately Illustrator doesn't have this, it always assumes that your monitor is 72ppi resolution. The problem with implementing custom monitor resolution in Illustrator is that it is a vector program and unlike Photoshop it doesn't have a ppi settings for its vector objects which are resolution independent. For the use of its rulers and numerical dimensions input when set to pixels, it has to assume an eventual ppi rasterization of the vector objects. If Illustrator uses the same feature like Photoshop then the same Illustrator file will show different pixel dimensions depending on which monitor it is displayed which may cause a much greater confusion than the problem you have now.
To find the physical size in Illustrator, right click on its ruler and set it to units that you have on a real life ruler. Then put the real life ruler on your screen and change the zoom level until the rulers in Illustrator are the same size as the real life ruler. Then write down the zoom level and use it again when you want to check the physical size of your work.
I think with your 109 ppi monitor, the zoom level should be about 152%

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