> On 15 Dec 2012, Robert hansen wrote: > > > One of his observations was that students will > accept > > that 0.333... is 1/3 but have trouble accepting > that > > 0.999... is 1. > > I wonder if "accepting" this would be a problem if > these students had been taught how to convert a > repeating decimal into a fraction, as we were when I > was in high school? > > Let x=0.999... > then 10x=9.999... > then 9x=9 > and x=1
When I taught Algebra I, I would show students the method you cited. Many students reacted as if it were a trick - like when one 'proves' that 2 = 1 by using an illegal divide-by-zero step.