To solve this expression, we can follow the order of operations (parentheses, exponents, multiplication and division, addition and subtraction) and simplify step by step:

Convert the fractions to decimals:
3 1/3 = 3.33
1 1/4 = 1.25

Perform the multiplication:
(3.33 - 1.25 * 0.24) + 0.4
(3.33 - 0.3) + 0.4

Perform the subtraction:
(3.33 - 0.3) + 0.4
3.03 + 0.4

Perform the addition:
3.03 + 0.4 = 3.43

Therefore, -0.9: 3 1/3 - 1 1/4 * 0.24 + 0.4 = 3.43.