1=0.999999999999999999999999999999999..., page-20

Let's break this down step by step.

We all know what 1/3rd is when you write it in decimal notation. It's like this:

0.333333333.....with a dot over the last 3, to tell you that it continues to infinity.

So- obviously we know that if we multiply 1/3 by three, that equals 1. With me so far?

Now, if we multiply 0.333333....repeating to infinity, by three, what do we get?

0.99999999...repeating to infinity.

But we've just seen that 1/3 multiplied by 3 equals 1.

Therefore, 0.9999999...repeating equals 1.

QED.