Interesting Things- Does 0.99999 is Really Equal to 1

Does 0.999 (repeated) equal “one”?  You might be surprised by the answer… which is “yes”.  I heard this on a couple of podcasts over the last few months, and I still find it hard to accept at face value.  However, I am now convinced and here’s several simple proofs that .99999 does indeed equal 1…

Method 1:

Let x = 0.9999…

Then 10x = 9.9999…

If we then subtract x from both sides of the equation, then:

10x – x = 9.9999… –  0.9999…

So, 9x = 9

Divide both sides of the equation by 9, and…

x = 1 … which, when we started, we said = 0.9999…

Method 2:

1/9 = 0.11111…

Multiply both sides of the equation by 9:

9 X 1/9 = 9 X 0.11111…

1 = 0.99999…