Aielyn on 03 April 2016
| MohammadBadir said: It's kinda hard to grasp. On one hand 0.33333 = 1/3 so 0.99999 should be 1, but on the other hand, it stars with 0 so it's technically an infinitesimal smaller :P |
It's not. Decimal notation with the "..." at the end (or a bar over the repeating part) is actually shorthand for a mathematical limit. What 0.999999... actually represents is
sum from n=1 to infinity of 9/(10^n)
And that evaluates to 1. The fact that it "starts with zero" is irrelevant. Decimal notation is nothing more than a representation, it's not actually a number. 0.1111.... represents 1/9. 0.9999.... represents 1.
