Using a higher dpi count for your image gets you no better resolution since the monitor can't display more pixes per inch than it has. My laptop, for example, has a 17" screen. At its highest resolution setting (1,600x900), that is 106 dpi (17" diagonal screen is 15" wide). Consequently, any resolution above 106 dpi for an image is lost since the monitor can't display 300 dpi.

The result is that you can save file size by reducing the dpi of the image to that of the monitor (~100 dpi). It won't change what you see on the monitor. Printing a picture is, of course, a completely different story since printers have much higher resolutions than monitors do