What does "very approximate" mean?

Solution 1:

I follow your reasoning, but the point of an approximation is that the exact answer is not available. So the salient feature is that it is not exact. Therefore, very approximate is used to mean very inexact.

An approximation which is especially accurate is a very close approximation. When this near-exactness is expressed in adjective form, I think the word approximate is generally avoided, in favor of phrases like almost exact or very nearly exact.

Solution 2:

The phrase makes sense, but there's definitely reasons to interpret it both ways.

Approximately really means "close", but people often interpret it to mean "my estimate."

When people say something is very approximate, it means they are using a lot of approximating (estimating) and very little fact.

Solution 3:

It's either approximate or precise. "Very" approximate means even less precise because "very" intensifies the approximation. We're talking ball park estimates, educated guesses. However, Mark Twain once said that authors should go through a manuscript and substitute "damn" for "very". Your editor will delete it and the text will not lose meaning. The safe thing to do is to refuse to use "very" except in rare and carefully considered circumstances.