This is a topic which I think is sometimes taught as an isolated technique within the curriculum. Perhaps converting recurring decimals to fractions is seen as the missing piece in the jigsaw of converting between fractions, decimals and percentages that students have learned at primary school. I think that the way this topic is approached depends on what the teacher thinks the point of it is. Modern calculators will do this conversion at the push of a button, so I think we are not teaching this topic to be ‘useful’.
This paper appears here with the permission of the publisher. This paper was published in the journal Scottish Mathematical Council Journal. The journal website is at: http://www.scottishmathematicalcouncil.org/wp1/smc-publications/journals/.