"Order of magnitude" for changes in prefix

Solution 1:

Consider thousandfold. The example in wiktionary is:

The changes to the algorithm resulted in a thousandfold increase in efficiency, earning the engineer a small brass plaque.

wiktionary also shows a plural, thousandfolds, but for purposes of approximation, go with thousandsfold instead. Example: "There was a thousandsfold increase in consumption when they added ingredient X."

Edit: Note that ngrams shows little use of either of thousandfolds or thousandsfold by comparison with thousandfold. Here are some examples of use of thousandsfold evinced in google-books references:

• "...the quantities will be reduced thousandsfold from the concentrations in the originally polluted areas." - "Nature out of place", Van Driesche & Van Driesche, 2004
• "By introducing pigs, rats, domestic plants ... they raised the biological colonization rate thousandsfold." - "The future of life", E. O. Wilson, 2003
• "... as if ... from the distance of the Falls of the Clyde (our little Scottish Niagara) with the body of water there thousandsfold increased..." - "Across Western Waves: America for Modern Athenians ...", Arthur Giles , 2007 reprinting of a previous-century book

Solution 2:

"Three orders of magnitude".

Or less precisely "orders of magnitude".

Or, still imprecise, and for larger orders "several orders of magnitude".

Note that for many people who are not mathematically literate an "order of magnitude" just means "a lot".