If you don't want to compare infinite decimal places, you can simply convert 0.3 to fraction instead of 1/3 to number:
![0.3 = (3)/(10)](https://img.qammunity.org/2019/formulas/mathematics/high-school/6rkrfuyni9hsgfn0f7azqvfc1vn5ziwi1p.png)
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:
![(3)/(10) = (3\cdot3)/(10\cdot 3) = (9)/(30)](https://img.qammunity.org/2019/formulas/mathematics/high-school/usl75j5y7q7kb4j6hlwdlmamps5c1z1dpt.png)
![(1)/(3) = (1\cdot 10)/(3 \cdot 10) = (10)/(30)](https://img.qammunity.org/2019/formulas/mathematics/high-school/x2cuf8rszb5x9ggewxr3nfk3gmm4ezvj59.png)
So, since 10/30 is more than 9/30, you can deduce that 1/3 is more than 0.3