how does .999999… repeating equal 1?

Question

I know there are proofs on this but I’m not great at math, can someone dumb it down for me?

In: Mathematics

Answer 1

A simpler explanation:

Let’s start with a simpler number, 0.9. How much different is 0.9 to 1? They differ precisely by 0.1.

Now, let’s add more trailing digits, 0.99. How much different is 0.99 to 1? They differ by 0.01.

You see, each trailing digit we add, the difference drops an order of magnitude. So, for 0.99999, the difference would be 10^(-5).

Now, let’s say 0.99999 goes on infinitely. What would be the difference between 0.9999 recurring and 1? It would be, according to our observation, be 10^(-∞), which would be 0.00000…. That number would be infinitesimal.

And hence, when two numbers have zero difference, those two numbers are the same.