It really depends on the particular application that is showing the image, but in general the DPI information is just ignored and the display size of the image is depending on its pixel dimensions.
For example a browser will (absent any specific scaling in HTML or CSS) show the image as 1200x900 pixels and the physical dimensions of that will depend on the PPI of the monitor. So with a PPI of 100, the physical size on the monitor will be 12x9 inch. If this is larger than the size of the monitor, the browser might scale it down for your convenience.
DPI only really matters when printing, and even then it may be ignored. E.g. if an image is embedded in a PDF or other layouted document, the effective DPI will depend on the physical dimensions specified in the layout.