To solve the expression \( 227.36 : (865.6 - 20.8 \times 40.5) \times 8.38 + 1.12 \), follow these steps:
Calculate the multiplication in the parentheses: \[ 20.8 \times 40.5 = 840.4 \]
Substitute back into the expression: \[ 227.36 : (865.6 - 840.4) \times 8.38 + 1.12 \]
Perform the subtraction: \[ 865.6 - 840.4 = 25.2 \]
Now the expression simplifies to: \[ 227.36 : 25.2 \times 8.38 + 1.12 \]
Perform the division: \[ 227.36 \div 25.2 \approx 9.004 \]
Then multiply by 8.38: \[ 9.004 \times 8.38 \approx 75.34732 \]
Finally, add 1.12: \[ 75.34732 + 1.12 \approx 76.46732 \]
Thus, the final result is approximately \( 76.47 \) (rounded to two decimal places).