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

> 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...