Should we use "in terms of"?

I have came across this reference: https://www.e-education.psu.edu/styleforstudents/c3_p35.html

This phrase is virtually meaningless, but we often hear it on the news and in bloated speeches. “In terms of” is really just a wordy and sloppy transition—usually an unoriginal disguise for a simple preposition, such as “in,” or a more elegant phrasing, such as “in relation to.” “In terms of the cost, it is high,” is easily revised to “Its cost is high.” Do not use “in terms of,” or do so trembling.

Is the reference really right?

Can I use the following sentence?

The figures are expressed in terms of a percentage/in percentage terms.

If so, the phrase "in terms of" seems not to be referred to relation.

I suppose the phrase could be just extra meaningless words. Instead of saying, "The figure is expressed in terms of a percentage", you could say, "The figure is expressed as a percentage". But using the phrase "in terms of" adds some emphasis.

The example from the quote, "In terms of cost, it is high", is just poor grammar. What is high? There is no proper antecedent for the pronoun.

Where the phrase is mainly useful is when the object being referred to is ambiguous. Like if I said, "The cost of this war was too high", you might well assume that I meant the financial cost. If I said, "In terms of lives lost, the cost of this war was too high," I clearly mean something very different. I could, of course, reword the sentence to avoid the ambiguous word. Like here I could say, "Too many lives were lost in this war." But perhaps I want to use the word "cost" to express the idea I am trying to convey in the larger context. That would be especially true if I was trying to establish a parallel construct, like, "In terms of dollars spent, the cost of this war was low. But in terms of lives lost, the cost was very high."

I suspect that Strunk & White, The Elements of Style influenced the treatment of "in terms of" in the Penn State University style guide for students, which the poster cites. In the chapter on "Words and Expressions Commonly Misused," Strunk & White, fourth edition (2000), offers this entry:

In terms of. A piece of padding usually best omitted.

The job was unattractive in terms of salary.

The salary made the job unattractive.

Strunk & White remains an extremely influential style book in the United States. It consistently prefers conciseness to prolixity, which puts it (to some extent) at odds with the conversational style increasingly popular in writing over the past several decades. Nevertheless, the core idea that writers shouldn't habitually write longer than they need to in order to express themselves clearly and effectively strikes me as sound—and respectful of readers' time.

The phrase "in terms of" is crucial to the sense of the sentence "Solve for x in terms of y." It is far less useful in the example that appears in the poster's original question, as zpletan illustrates by saying the same thing more succinctly in a comment beneath that post. It is utterly expendable in the example that Strunk & White provides.

Like most other style guidelines, the stricture against "in terms of" is not absolute. But if you're aware that "in terms of" frequently is superfluous—or at least long-winded—you can tighten your writing by taking care to use it only when it contributes something meaningful to your prose.

I personally think it is a useful usage when discussing large or complex subjects which could be viewed/analysed/approached from a variety of perspectives. In that sort of scenario I might be looking at say, the state of the nation, from the the viewpoint of a poor child and not in terms of GDP.

But like 'obviously', 'literally'et al, it is susceptible to mangling by fools.

Yes you can. Your usage of "in terms of" is completely different. You are specifying the scale on which the quantity is being represented. It's obviously important to specify this so as to make clear the distinction between an absolute scale (pure numbers) and relative scale (percentages and fractions).

The style manual suggests a usage of "in terms of" that seems unneccesary -- where the phrase is merely used as a connecting phrase. I've encountered some equally jarring transitions, such as "If we consider the exchange rate, we find that it has increased", where the initial clause is just a clumsy introduction to the main observation. Note that these constructs are perfectly grammatical, but they just don't reflect good style. They also notch up the often constrained word count in academic papers.

I think if "in terms of" describes the units or metrics used then it's a valuable idiom. E.G. We evaluated the project in terms of sales and customer count.

When used to mean "with reference to" then it hurts my ears but is acceptable. E.G. In terms of success, we exceeded our wildest dreams.

When used out of pure laziness or in terms of inability to form a sentence, it is just wrong.