how to resize an image in adobe illustrator

How can I solve this problem as I want to size a photo and 'place' it into illustartor at the correct size and at 300dpi so that I can print it! 900px x 900px, the resolution starts to decrease and do so drastically! However what actually happens is the 'placed' image appears but is over four times smaller in illustrator!! In itself this isn't a problem but then when I scale it up to the size I want e.g. Now I would expect the 'placed' jpeg to cover the entire artboard in illustrator because the jpeg is 900px x 900px and so is the artboard. I then opened an illustrator document setup to 900px x 900px at 300ppi and 'placed' the red jpeg I had just created in photoshop into illustrator. I then saved this image as a jpeg so the jpeg had a dimension of 900px x 900px. To give an example I just created a photoshop canvas of 900px x 900px with a resolution of 300ppi and filled it with a red colour. Hi when i size an image in photoshop and then 'place' it in illustrator the 'placed' image is way smaller in illustrator than in photoshop.

How to resize an image in adobe illustrator