A fraction of fractions

On Twitter I encountered a dialogue about the use of fractions, and the question whether we should consider “three tenths” as something different from 0,30 (or 0.30), and whether that differs from 0.3 (or 0,3 ;-). I would think this makes a difference.

Some sources on fractions (only a small selection):

This PhD research was about fractions in primary and secondary education. Unfortunately the thesis is not available digitally. There is, however, a blog where the author has posted some more information.

This document gives an overview of  issues concerning (decimal) fractions on pages 7 and 8, for example place value. In Dutch: this webpage. I also remembered these critical remarks about so-called TAL booklets.
Wu has also written about this topic, and probably more people. Please mention them in the comments!