EDIT:
So to sum up a digital file does not actually have a size until it is printed and that printed size will depend on the ppi set in the document box, it only has pixel dimension which never change (unless resampled) which in itself is not a physical size.
Very good summary. (Paul posted while I was preparing what follows) .
You need to click Resample Image.
In order to change the size of the image the software has to reduce the number of pixels. If it is reducing the size, as in this case, it needs to go round the image taking a bunch of pixels at a time and crunching them into a single pixel in the resized image. This is resampling.
In this case it produces each new pixel from about 37 pixels in the full size image.
Here we go. This is in Photoshop CS2, but I'm sure it will be the same in Elements.
Here is an image which is 5760 x 3840 at 240 pixels per inch. As you can see, this is 60.96 cm x 40.64 cm, and the rulers at the top and left are consistent with this. You can see from the bottom left hand corner that we are viewing the image at about 17% of full size so as to get it all in the window.
Resize example - before resize by
gardenersassistant, on Flickr
With Resample Image ticked, I changed the Width to 10cm. When you do this the numbers in the dialog box immediately change to those shown below. (In fact in this case I clicked OK to actually make the change so the rulers would reflect the new size. I then went back to the resize dialog to get this screen capture.)
Resize example - after resize by
gardenersassistant, on Flickr
As you can see, we are now looking at the image 100%, and the dialog box and the rulers show it as 10cm wide.
Notice that in terms of pixels, the image is now only 945 pixels wide and 630 pixels high. The arithmetic is easier to follow if you change the dialog box to show pixels per cm rather than pixels per inch.
The image had 240 pixels per inch. From the above image we can see that this is 94.5 (near enough) pixels per cm. So at 94.5 pixels per cm, the 10 cm wide version of the image is 945 pixels wide.