> > 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. > > Richard
I do not remember any of my classmates thinking that this was a trick because we had converted all sorts of repeating decimals to fractions,e.g. 2.3... 3.6868... 4.32525...
