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I was stumbling upon the "Smallest width" settings. It seems increasing this value will make everything show up smaller on the screen and vice versa.

What does it mean and what's its function?

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Here is the relevant excerpt from https://developer.android.com/training/multiscreen/screensizes.

The "smallest width" or "minimum width" screen size qualifier allows you to provide alternative layouts for screens that have a minimum width measured in density-independent pixels (dp or dip).

By describing the screen size as a measure of density-independent pixels, Android allows you to create layouts that are designed for very specific screen dimensions while avoiding any concerns you might have about different pixel densities.

The smallest width qualifier specifies the smallest of the screen's two sides, regardless of the device's current orientation, so it's a simple way to specify the overall screen size available for your layout.

Here's how other smallest width values correspond to typical screen sizes:

320dp: a typical phone screen (240x320 ldpi, 320x480 mdpi, 480x800 hdpi, etc).
480dp: a large phone screen ~5" (480x800 mdpi).
600dp: a 7” tablet (600x1024 mdpi).
720dp: a 10” tablet (720x1280 mdpi, 800x1280 mdpi, etc).

Remember that all the figures for the smallest width qualifier are density-independent pixels, because what matters is the amount of screen space available after the system accounts for pixel density (not the raw pixel resolution).

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