Final answer:
To calculate a rectangular room's area and its uncertainty, multiply the measurements of length and width, then determine the uncertainty based on the relative uncertainties of these measurements. The example provided results in a room area of 12.0 m² with an uncertainty of 0.4 m².
Step-by-step explanation:
To calculate the area of a rectangular room and its uncertainty, you need to use the measurements of length and width provided, including their uncertainties. If a room is measured to be 3.955 ± 0.005 m in length and 3.050 ± 0.005 m in width, you multiply these two measurements to find the area. The uncertainty is found by adding the relative uncertainties of the length and width measurements before multiplying by the calculated area.
For instance:
Calculate the nominal area: Area = Length x Width = 3.955 m * 3.050 m = 12.06275 ㎡
Calculate the relative uncertainties: (0.005/3.955) + (0.005/3.050) ≈ 0.0013 + 0.0016 = 0.0029
Calculate the area uncertainty: 12.06275 ㎡ * 0.0029 (rounded to 0.003 for simplicity) = 0.03618825 ㎡, which rounds to 0.4 ㎡ when considering that the area is given to a tenth of a square meter.
Therefore, the area of the floor is 12.0 ㎡ with an uncertainty of 0.4 ㎡.