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Topic: Why is there a difference between fractions 1/3 and .333 repeating
multiplied by 3

Replies: 10   Last Post: Oct 2, 2017 10:26 PM

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 mitchrae3323@gmail.com Posts: 146 Registered: 9/12/17
Re: Why is there a difference between fractions 1/3 and .333
repeating multiplied by 3

Posted: Oct 2, 2017 2:33 PM

On Monday, October 2, 2017 at 4:59:22 AM UTC-7, FromTheRafters wrote:
> mitchrae3323@gmail.com explained :
> > Multiply by three 1/3 takes you to One and .333 repeating takes you to .999
> > repeating. Why would they create an infinitely small quantity difference?
> >
> > Mitchell Raemsch

>
> They don't. Repeating decimal expansions are merely decimal expansions
> of rational numbers.
>
> One quarter is 1/4 or 0.25000... or 0.24999...

They share a sameness because they are infinitely close; with no in between quantity...

> these representations
> all represent the same rational number. There are no rational numbers
> between 0.999... and 1.000... and there are always rational numbers
> between two 'different' rational numbers, so we are left with equality.

You reach an infinitely small difference of quantity that would not reduce.
You are left with an infinitely small difference...

Mitchell Raemsch