Date: Dec 27, 2012 8:17 PM
Author: Domenico Rosa
Subject: Re: A Point on Understanding
> > 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
> > 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.
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.