1) A rectangular rug has a length of 231 centimeters and a width of 166 centimeters. What is the area of the rug in square meters? Explain how you determined the correct number of significant digits for your answer.
2) Christina swims 2400 feet in 16 minutes. Gloria swims 12 meters in 15 seconds. Whose average speed is faster? Explain. Use 1 meter ≈ 3.28 feet.
I think Christina's average speed is faster.
2.31 * 1.66 = _______ square meters
(2400 / 3.28) / (16 * 60) = _______ meters per second
12/15 = ______ meters per second
1) To find the area of a rectangular rug, we multiply its length by its width. Given that the length of the rug is 231 centimeters and the width is 166 centimeters, we can calculate the area as follows:
Area = length × width
Area = 231 cm × 166 cm
Now, to convert the area from square centimeters to square meters, we need to divide the area by the conversion factor of 10,000 (since there are 10,000 square centimeters in a square meter):
Area = (231 cm × 166 cm) / 10,000
Simplifying this equation gives us:
Area = 38346 cm² / 10,000
Area = 3.8346 m²
Now, let's consider the significant digits in our final answer. The number 3.8346 has five significant digits, but since we obtained this value by multiplying two measurements given to three significant digits (231 cm and 166 cm), the final answer should have no more significant digits than the least number of significant digits in the original values. In this case, both measurements have three significant digits, so our final answer should have three significant digits as well.
Therefore, the area of the rug is 3.83 m², rounded to three significant digits.
2) To compare the average speeds of Christina and Gloria, we need to calculate their speeds in meters per second.
First, let's convert Christina's distance from feet to meters. Using the conversion factor stated in the question (1 meter ≈ 3.28 feet), we can convert the distance as follows:
Christina's distance in meters = 2400 ft × (1 m / 3.28 ft)
Calculating this gives us:
Christina's distance in meters = 731.71 m (rounded to two decimal places)
Now, let's calculate Christina's average speed using the given time of 16 minutes:
Christina's average speed = Christina's distance / time
Christina's average speed = 731.71 m / 16 min
Since the time is in minutes, we need to convert it to seconds:
Christina's average speed = 731.71 m / (16 min × 60 s/min)
Simplifying this gives us:
Christina's average speed = 731.71 m / 960 s
Calculating this results in:
Christina's average speed = 0.761 m/s (rounded to three decimal places)
Now, let's calculate Gloria's average speed using her given distance of 12 meters and time of 15 seconds:
Gloria's average speed = Gloria's distance / time
Gloria's average speed = 12 m / 15 s
Calculating this gives us:
Gloria's average speed = 0.8 m/s
Comparing their average speeds, we can see that Christina's speed is 0.761 m/s, while Gloria's speed is 0.8 m/s. Therefore, Gloria's average speed is faster than Christina's.
Note: In this comparison, we didn't consider significant figures since they are not relevant to this specific calculation.