How to write 3?

One trick I learnt long ago was to convert recurring decimal numbers into fractions.

For instance, how does one write 2.333333... as a fraction. Simple,
let x = 2.33333...
10x = 23.33333...

subtract the two equations and we have 9x = 21. Thus we have x = 21/9 or 7/3.
There we have it 2.3333... is 7/3.

Another example, say my number is 2.345345345...
let x = 2.345345345...
1000x = 2345.345345345...

subtract the two equations and we have, 999x = 2343. Thus x = 2343/999 = 781/333.
There 2.345345... = 781/333.

Now lets try 2.99999...
x = 2.9999....
10x = 29.99999...

subtract the two equations and we have 9x=27. Thus, x = 3!!!

What went wrong? Ofcourse 2.99999.... cannot be equal to 3 its less than 3.
I remember going to my school teacher with this problem. I showed him this and
what he told me was amazing.

The truth is 2.9999.... = 3. Its just another way of writing the same number.
You could either write three as 3.0000000.... or 2.9999999... both forms are
correct. We have chosen the former only for simplicity.

The first time I learnt this I was quite shocked. The number line is a continuum.
You could approach 3 from either direction.