The best thing to do in this case is to adjust your settings to take screenshots at a higher resolution.
Taking screenshots at 150 pixels per inch should usually be adequate for getting screenshots to show up clearly at full page width in a Leanpub book or course.
How you set the resolution for screenshots will depend on the resolution of the screen on your device, and on the tool you are using to take screenshots on your device. A quick Google search should help you find instructions for adjusting your screen resolution settings on your device and the version of your operating system.
If you are going to be taking lots of screenshots, you may want to consider getting a special app for taking and editing screenshots, like Snagit, which is what we currently use for screenshots in our Help Center articles and manuals.