Which is bigger: 0.3 or 1/3

First, turn the fraction into a decimal to get a better look at the problem. To do that, divide the numerator (top half) by the denominator (bottom half). 1 divided by 3 = 0.33
0.33 is larger than 0.3. If it helps, add a 0 to 0.3 to get 0.30 and you'll see that 33 is in fact a larger number than 30. (Adding the zero does NOT change the number, it holds no place value it's just there for looks.)