DPI isn't a meaningful measurement of image size/resolution in this situation. DPI is a ratio between the number of dots (pixels) in the image and the number of inches those pixels are spread out over. You can know the number of dots, but the "per inch" part doesn't occur until the image is printed. A 1000 pixel image printed at 1 inch is a 1000 dpi image; same image printed at 10 inches is a 100 dpi image.
Some image file formats carry DPI information that suggests a printing size for the image. If our example 1000 pixel image claims to be 100 dpi, then many programs will size the image to 10 inches (1000 dots / 100 dpi = 10" ) when you import the image.
When the image format doesn't allow for preserving DPI info, the application might use a default of 72 dpi (common on Macs) or 96 (common on Windows PCs, though sometimes it's 120 or other values). Or the application might use some other way of sizing the image.
In any case, you can see what Irfanview thinks by pressing I. That'll show you lots if info about the image, including DPI (which you can change if you like) and the size that the image will print IF using a print setting that sizes the image based on image pixes/dpi.