# Thread: Representing 0.999999999... as an integer fraction

1. ## Representing 0.999999999... as an integer fraction

Well I just decided to refresh my math skills so started to reread an old Calculus book I have had for a while.

I came across an end of chapter problem that inquired whether
0.999999... < 1.0000000

It asked to represent 0.9999999... as a fraction of integers to arrive at an answer

So I did this

x = 0.9999999999

100 x = 99.9999999999
- x = - 0.9999999999
99x = 99
x = 1

The second part of the question referred to finding a real number between 0.9999999999 and 1.000000000

So I did this 1/2(0.9999999999+1)
=1/2(1.9999999999)
=0.9999999999

Why would I get 1 when I tried to represent 0.9999999999... ( is it a rational number with repeating digits) as a fraction of integers

2. Do you understand that there is a difference between $0.99999$ and $0.99999\cdots=0.9999\overline{9}$?
Now $0.999999$ is a number between those two.

3. Originally Posted by Plato
Do you understand that there is a difference between $0.99999$ and $0.99999\cdots=0.9999\overline{9}$?
Now $0.999999$ is a number between those two.
Actually I didn't understand the difference thus the confusion

So then, how would I represent 0.99999 as a fraction of two integers.

4. Originally Posted by dexteronline
Actually I didn't understand the difference thus the confusion

So then, how would I represent 0.99999 as a fraction of two integers.

Do you know how to represent 0.9 as a fraction? 0.99? 0.999? etc. ....

5. Originally Posted by mr fantastic
Do you know how to represent 0.9 as a fraction? 0.99? 0.999? etc. ....
LOL

I think I meant to ask how to represent 0.99999... ( an infinite seires of 9s ) as a fraction of two integers
I am too slow to understand things, please don't be angered if I sound dumb

6. Originally Posted by dexteronline
LOL

I think I meant to ask how to represent 0.99999... ( an infinite seires of 9s ) as a fraction of two integers
I am too slow to understand things, please don't be angered if I sound dumb
You found that 1 = 0.9999999......... did you not? So what's wrong with giving 1/1 as the answer?