1. ## 0.999... = 1?

I can't seem to figure out what I am doing wrong

express in form a/b

0.9 (bar)

So I start...

x = 0.99999...
10x = 9.9999...

LHS:
10x - x = 9x

RHS:
9.9999 - 0.9999 = 9

so 9x = 9

thus x = 1

So now I am stuck and can't seem to figure out where I went wrong... plz help

2. Originally Posted by Solan
I can't seem to figure out what I am doing wrong

express in form a/b

0.99 (bar)

So I start...

x = 0.99999...
10x = 9.9999...

LHS:
10x - x = 9x

RHS:
9.9999 - 0.9999 = 9

so 9x = 9

thus x = 1

So now I am stuck and can't seem to figure out where I went wrong... plz help

That is correct for that method. Another way is this

$\displaystyle .9999=\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+.. .=\sum_{n=0}^{\infty}\frac{9}{10^{n+1}}$

$\displaystyle \frac{9}{10}\sum_{n=0}^{\infty}\frac{1}{10^n}=\fra c{9}{10}\cdot \frac{1}{1-\frac{1}{10}}=\frac{9}{10} \cdot \frac{10}{9}=1$

Good luck.

3. Originally Posted by Solan
I can't seem to figure out what I am doing wrong

express in form a/b

0.9 (bar)

So I start...

x = 0.99999...
10x = 9.9999...

LHS:
10x - x = 9x

RHS:
9.9999 - 0.9999 = 9

so 9x = 9

thus x = 1

So now I am stuck and can't seem to figure out where I went wrong... plz help
You're not wrong. So the answer to the question is 1/1.