Yes, so I was wrong. Wee Chern told me a few days back that the recurring decimal of 0.9999…. is equals to 1 exactly and I refused to believe him, highlighting that it will go on and cannot be rationalized. It is, perhaps against intuition to think that they are both equal given that recurring decimals are uncommon figures that we never thought would be rationalized, though we do know they can be expressed as fractions most of the time – and this is key to proving this seemingly absurd relation.

I can’t believe how simple this is and we simply can’t accept it for the first time we see the relation:

1/3 = 0.333333……

Multiply both sides by ‘3’.

3 * 1/3 = 3 * 0.333333……

Hence,

1 = 0.999999……

Mathematics have to be weird sometimes to challenge our intuition, just like the Monty Hall Problem.