If it's just 0.3, it's 3/10, as the 3 is simply moved after the decimal point once.
However, if youre talking about 0.3333... (3 repeats forever), then it's 1/3, and we can use math to prove it. Each time you divide 3 into 1, it's impossible, so you always borrow a 0 from the next decimal place. That always returns 1, and we can see that it becomes recursive. Therefore, we are left with a repeating decimal, which is represented in a fraction as 1/3.