Date: Dec 27, 2012 9:24 AM
Author: Richard Strausz
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