Math Is Fun Forum

goddess

Member

Registered: 2005-03-12

Posts: 4

does 0.9 recurring = 1?

it is thought that :
x=0.9...
10x=9.9...
9x=9
so
x=1

but if you do 1+1 you get 2 and with 1+0.9 you get 1.9...

goddess

Member

Registered: 2005-03-12

Posts: 4

Re: does 0.9 recurring = 1?

it had to come up some time
please help

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: does 0.9 recurring = 1?

Welcome, Goddess.

Well, I guess that is the thing about mathematics. It's gotta work all the time!

I suppose you read our page on 9 Recurring

Well, let us try with your variation: Does 1 + 0.999... = 2 ?

Let X = 0.999...
   
So, we are asking: Does 1+X = 2 ??

Let's start with: 1+X = 1.999...

Multiply by 10:  10(1+X) = 10(1.999...)
Or: 10+10X = 19.999...

Subtract X from each side to give us: 10 + 9X = 19.999... - X

but we know that X is 0.999..., so: 10 + 9X = 19.999... - 0.999...
or: 10 + 9X = 19
or: 9X = 19-10 = 9
or: X = 9/9 = 1 

So, X is equal to 1 and also equal to 0.999... (because we said so at the top)

Therefore 0.999... = 1

---

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

goddess

Member

Registered: 2005-03-12

Posts: 4

Re: does 0.9 recurring = 1?

thank you