1. The problem statement, all variables and given/known data Four positive numbers, each less than 40, are rounded to the first decimal place and then multiplied together. Use differentials to estimate the maximum possible error in the computed product that might result from the rounding. 2. Relevant equations dz=(dz/dx)dx+(dz/dy)dy 3. The attempt at a solution I know that the solution to this problem is 4(40)^3(0.05)=12800 and I know how to apply the formula for differential to get that answer. But I'm having trouble understanding WHY this answer is correct. I tried out this question using numbers closest to 40 that I could get when rounded to the first decimal place. I used 39.85 for the four numbers. When rounded off, this gives us 39.9. So I computed the error that would result like so: (39.9)^4 - (39.85)^4= 12680.37959 However, the correct answer is supposed to be 12800. I chose the closest possible numbers to 40 that I could, and I used the maximum possible error from rounding to the first decimal place (0.05). I would really appreciate it if someone could help me figure out what I'm doing wrong. Thanks!!