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Multiple drawables background images to fit the screen resolutions

Alright, so I have an image that it's resolution is: 1054X1054. I want to set that image so it fits exactly the screen size of the android devices. (I'll cut the image in some editor as nessacary). So my question is: How can I know what resolution my image should be so it will cover the device background without needing to resize the image.(For the mdpi,hdpi,ldpi)

I'm asking that question because I keep missunderstanding how the "multiple screen resolutions" really work..

you can design your image to re-size with different screen sizes, you'll discover that each design requires a minimum amount of space. So, each generalized screen size above has an associated minimum resolution that's defined by the system.

android os count sizes in "dp" units—the same units you should use when defining your layouts—which allows the system to avoid worrying about changes in screen density.

xlarge screens image sizes are at least 960dp x 720dp
large screens image sizes are at least 640dp x 480dp
normal screens image sizes are at least 470dp x 320dp
small screens image sizes are at least 426dp x 320dp

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