Is "600% smaller" correct use of percentages?

Solution 1:

This statement is likely correct about whatever file format you're talking about. To understand why, you have to look at the savings as a ratio.

Imagine you have a file that is 1,000,000 bytes of raw data, and you compress it with GIF, and the result were 900,000 bytes of compressed data. Now, imagine the other file format takes the same 1,000,000 bytes and outputs 400,000 bytes of compressed data.

The original GIF encoding saved 100,000 bytes, the new file format saved 600,000 bytes of data. As such, the new file format saved 600% space compared to the 100% space saved by GIF.

Note, we're not talking about the reduction in file size as a percentage of the original size, we're talking about the amount of space we saved in two different formats, which is a gain in efficiency, and that gain can be expressed as a ratio, and ratios can be expressed as percentages.

Solution 2:

It is meaningless. Something cannot be more than 100% smaller.

It would be like having a pint glass full of beer and then pouring away 6 pints of it!