A carpet layer measures a room to be 4.6 m long and 3.2 m wide. He multiplies the 2 measurements and reports the area of the room to be 14.72. what 2 things are wrong with this answer?

Answer 1

The carpet layer made two errors in calculating the area of the room:

1. Calculation Error: The area of a rectangle is calculated by multiplying the length by the width. In this case, the correct calculation should be: \[ \text{Area} = 4.6 , \text{m} \times 3.2 , \text{m} = 14.72 , \text{m}^2 \] However, on recalculating: \[ 4.6 \times 3.2 = 14.72 \] Although this appears correct, if an initial miscalculation was made with the figures, the correct area actually is: \[ 4.6 \times 3.2 = 14.72 , m^2 \] The measurement is indeed correct, but that's the right area. It's more that if the reference calculation was wrong, he truly should have done it correctly.

2. Significant Figures: The measurements of the length (4.6 m) and width (3.2 m) each have 2 significant figures. When multiplying these values, the final answer should also be reported in 2 significant figures. Thus, the area should be reported as: \[ \text{Area} = 15 , \text{m}^2 \] (when rounded to 2 significant figures rather than leaving it as 14.72).

In summary, the area should be reported as 15 m² due to significant figures, and it is the assumption of correctness or possibly continuous miscalculation.