Final answer:
The area of a rectangular garden plot with dimensions of 36.7 cm by 128.8 cm is calculated by multiplying the length by the width and the result is 0.472 square meters when expressed in the correct number of significant figures.
Step-by-step explanation:
The area of a rectangular garden plot can be calculated by multiplying its length by its width. Given a rectangular plot with dimensions 36.7 cm by 128.8 cm, the area in centimeters squared is found by performing this multiplication. However, we need to convert this area into square meters. To do this, we know that 1 square meter is equal to 10,000 square centimeters. So, we divide the product of the length and the width by 10,000 to convert it into square meters.
We'll start by multiplying the length and the width: 36.7 cm * 128.8 cm. This gives us the area in square centimeters. Then, we divide by 10,000 to convert the area to square meters.
The calculation is as follows: 36.7 cm * 128.8 cm = 4,724.16 cm². To convert to square meters, 4,724.16 cm² ÷ 10,000 = 0.4724 m². When expressing the answer in the proper number of significant figures, since we started with numbers that were to one decimal place, our final answer should also be to one decimal place if possible. Thus, the area of the garden plot in square meters, expressed with the correct significant figures, is 0.472 m².