Here are three files. They are all the same pixel dimensions (1600 x 2400). One is set to 1 dpi, another is set to 173 dpi and the last one is set to 900 dpi. If you download all three files you will see that they are exactly the same size. On disk they are around 420K (give or take a few K depending on your storage device). Open all three in photoshop and you will see that they are the same. You can even stack any two of them as separate layers in the same Photoshop document and set the top layer to difference mode and see that they are the same.
Where you would see a difference is if you placed these files into an InDesign document. The 1dpi image would be gigantic (1600x2400 inches) and extremely pixelated. The 173 dpi image would be about 9x14 inches and decent resolution. The 900 dpi would be a little bit smaller than 2x3 inches. But all of the files are the same size (~420K) and if you resized them all in InDesign to be 4x6 inches they would all be 4x6 inches at the same resolution (400 dpi).