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human
Are huge compression ratios attainable in specific cases?

Ive been doing a bit of online research and the only things i seem to be finding are on general compression algorithms with ratios of 20-35% But is it possible to achieve much greater ratios in specific cases? 

Im not well educated in this field and im probably missing something but even basic math expressions seem to "encode" information with way more efficiency than general compression algorithms.

2.1514733e+97 for example can be expressed as (27\^68). 

compressing nearly 100 digits to just 4 and a symbol.

I feel like im failing to see something here or ive missed some obvious principle so any insights would be greatly appreciated.
gpt
Yes, it is!

The concept of Kolmogorov complexity might appeal to you. Consider that some photos may have simpler descriptions than others. Even if the description is made unambiguous (or, to use the proper term, "lossless") it is pretty easy to guess that any photo that is exactly one color over the entire set of pixels is easier to describe than a photo where each pixel is independently chosen at random.

The trick is to come up with a "language" of description where all the things you see most frequently have short descriptions, even if the things you see rarely might have longer ones. This is precisely what compression is all about.

Zip files are an example of this: they build a dictionary of words to describe the file as the file is scanned, which allows things the method "reads" to immediately reuse the index of a word in the dictionary instead of the entire word.

Even in jpeg, which is "lossy," care was taken so that the description of an image still results in something that looks very very much like the original data, even if it's not bit for bit the same.

Excellent question!