Do you mean the file size? - or the dimensions.
The file size you can reduce by increasing the jpeg compression. As you increase it the quality will decrease. If you experiment, you can reach the best balance between quality and file size.
The dimensional size, you can reduce by *resizing* - this can be done in most photo manipulation software, You can usually choose what units to use for the resizing - in/cm/pixels. If you reduce the dimensions of the photo, you will, of course, also reduce the file size.
The scanning resolution has nothing to do with all this - except in that the higher resolution you scan with, the larger the file size of your scan will be. Also the moer colours you use, the larger the file size will be.
It's unnecessary to scan average size things at more than 300dpi - any higher if really for scanning small objects that you want to reproduce in larger sizes.
Remember always that on a 17" display with a resolution of 1024x768 pixels, the display resolution is approx 13"/1024pixels = 80dpi - yes that's what you read - 80dpi.
So you can see how little very high scanning resolutions help with pictures for display on a monitor.