Science is all about measuring and counting, and expressions that indicate whether a given figure (quantity) is precise or rounded off are common in all science writing. Although several such expressions mean more or less the same thing, there are subtle differences, and a careful writer takes these differences into account.
About and Approximately For reasons that have been linked to the number of fingers we have – five on each hand – numbers are usually rounded off to multiples of five or ten. It is this characteristic that makes the following sentence sound odd: "Each plot contained about 17 trees." The apparent contradiction here is that 17, not being a multiple of 5 or 10, does not sound like a number that has been rounded off and yet it is qualified by the expression about. At the same time, the writer of the above sentence wanted to emphasize that the figure was not exact, in which case the better word would be approximately. Here is what the book Use the Right Word has to say about the difference: "About is often used interchangeably with approximately, but it does not stress the closeness to accuracy that approximately does."
About and Around The difference between about and around is more straightforward and largely a matter of preference: about is more common in British English and around in American English (Pocket Fowler's Modern English Usage, p. 8).
["Publish and prosper" is a series of posts about tips for researchers whose first language is not English but who submit papers to journals published in English. The series touches upon not only writing (spelling, grammar, punctuation, usage, and style) but everything else relevant to publishing research papers that journal editors wish their authors knew.]