Final answer:
To cover the floor, you'll need a carpet with an area of 14 square meters. When dealing with measurement uncertainties, the calculation is based on both the length and width uncertainties, which are then applied to the room's area.
Step-by-step explanation:
Calculating Carpet Area and Uncertainty
To calculate the area of the carpet needed to cover a floor, you need to multiply the length by the width of the room. Given the measurements are 4 m long and 3 m 50 cm wide, you convert the centimeters to meters, getting 3.5 m for width. Therefore, the carpet area needed will be 4 m × 3.5 m = 14 square meters.
When considering the uncertainty in measurements, if the length and width of a room are measured with uncertainties, the area's uncertainty is calculated using the formula: (relative uncertainty in length + relative uncertainty in width) × area of the room. For example, if measurements are 3.955 ± 0.005 m and 3.050 ± 0.005 m, and the uncertainties are 0.005/3.955 and 0.005/3.050, respectively, the uncertainty in the area can be calculated and, if necessary, rounded to an appropriate level of precision.
In a more general concept, when calculating the area of rooms or items in practical situations, typically only the significant figures are retained which are meaningful for the purpose, such as in house construction, decoration, or science experiments, to ensure efficient use of materials and resources.