Question
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?
Answers
GPT-4o mini
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.
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.