Question

prove that is 0.9=1

Answer 1

ANSWER SHOULD
it means that ans 0.9=1 APPROX

Answer 2

Let X = 0.999...

 

Then 10X = 9.999...

 

Subtract X from each side to give us:

   

9X = 9.999... - X

 

but we know that X is 0.999..., so:

   

9X = 9.999... - 0.999...

or:

9X = 9

 

Divide both sides by 9:

   

X = 1

 

But hang on a moment I thought we said X was equal to 0.999... ?

Yes, it does, but from our calculations X is also equal to 1. So:

   

X = 0.999... = 1