Decimals to Hundredths · Superchallenge problem

Lily rounds a number in two steps: first to the nearest tenth, then that answer to the nearest whole number. Max rounds the same number straight to the nearest whole number. (Both round halves up, so $0.45$ becomes $0.5$ and $0.5$ becomes $1$.) How many numbers between $0$ and $5$ with exactly two digits after the decimal point give Lily and Max different answers?