the best and the easeist solutionn0 root needed)
I pinpointed the problem to thumbnails. These are tiny copies of photos used by some apps to more quickly display pictures. Specifically, the 1GB was being taken up by a thumbnail index file, and I didn't need to lose that 1GB to a function I don't use on the tablet. I erased the file as follows:
1. Open a file manager on Android. I use any File Manager ES is the best.
2. Ensure that it can display system or hidden files. This is an option somewhere under Settings. In File Manager, tap Menu > Settings > Show Hidden Files.
3. Navigate to \mnt\sdcard\DCIM\ .thumbnails. By the way, DCIM is the standard name for the folder that holds photographs, and is the standard for pretty much any device, whether smartphone or camera; it is short for "digital camera IMages." Another BTW: when a folder name is prefixed with a period, then it is a hidden folder in Android (such as .thumbnails).
4. Select and erase the file that's about 1GB and contains the word 'thumbdata." The exact file name will vary.
After I did this, image viewing apps like Gallery operated just fine, with no apparent slowdown from the loss of this file.
In this way I freed up 1GB on my Android v4 tablet, 1GB on my Android v4 phone, and 750MB on an older Android v2 phone.
Keeping the 1GB Free
That's great if it works, but on my tablet, after deleting the file and creating a dummy file, the space STILL was never regained. The only way to get it back was a factory reset followed immediately by replacing the thumbdata files with empty folders of the exact same name. Since I did this, I've had no issues whatsoever and it's impossible for the OS to rob my tablet of space like it did previously.