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## #1 2005-03-12 01:13:48

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...

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## #2 2005-03-12 01:15:12

goddess
Member
Registered: 2005-03-12
Posts: 4

### Re: does 0.9 recurring = 1?

it had to come up some time

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## #3 2005-03-12 09:28:31

MathsIsFun
Registered: 2005-01-21
Posts: 7,664

### 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 ??

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

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## #4 2005-03-12 22:14:51

goddess
Member
Registered: 2005-03-12
Posts: 4

thank you

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