If you don't want to compare infinite decimal places, you can simply convert 0.3 to fraction instead of 1/3 to number:

So, the question now becomes: which is bigger, 1/3 or 3/10?
You can find the answer by giving the same denominator to both fractions:


So, since 10/30 is more than 9/30, you can deduce that 1/3 is more than 0.3