The distance between two cities is described as 260 kilometers. What is this distance in miles? Make an estimate first, explaining your reasoning briefly. Then calculate your answer using the fact that 1 in. = 2.54 cm. Remember to round your answer appropriately: The way you write your answer should reflect its accuracy. Your answer should not be reported more accurately than your starting data.
- A classroom has a floor area of 600 square feet. What is the floor area of the classroom in square meters? Describe three different correct ways to solve this area problem. Each way of solving should use the fact that 1 in. = 2.54 cm. Explain your reasoning.
The Correct Answer and Explanation is:
Part 1: Converting 260 Kilometers to Miles
Estimate:
To estimate the distance from kilometers to miles, we can use the approximation:
1 kilometer ≈ 0.6 miles
So:
260 km × 0.6 ≈ 156 miles
This is a rough estimate.
Exact Calculation Using 1 in. = 2.54 cm:
First, we need to convert kilometers to inches, and then from inches to miles.
1 km = 1,000 meters
1 meter = 100 cm
1 inch = 2.54 cm
1 mile = 63,360 inches
So:
260 km
= 260 × 1,000 × 100 cm
= 26,000,000 cm
= 26,000,000 ÷ 2.54 inches
≈ 10,236,220.47 inches
= 10,236,220.47 ÷ 63,360 miles
≈ 161.5 miles
Answer: The distance is approximately 162 miles (rounded to 3 significant digits, matching the 260 km precision).
Part 2: Converting 600 ft² to m² Using 1 in. = 2.54 cm
We will show three correct methods to convert 600 ft² to square meters, using the basic fact:
1 inch = 2.54 cm
Method 1: Convert Feet to Inches, Then to Centimeters, Then to Meters
1 foot = 12 inches
So:
600 ft² = (12 inches)² × 600 = 144 in² × 600 = 86,400 in²
Now convert square inches to square centimeters:
1 in = 2.54 cm → 1 in² = (2.54)² cm² = 6.4516 cm²
So:
86,400 in² × 6.4516 cm²/in² ≈ 557,450.24 cm²
Convert to m²:
1 m² = 10,000 cm²
→ 557,450.24 ÷ 10,000 ≈ 55.7 m²
Method 2: Convert 1 ft to Meters, Then Square
1 ft = 12 inches = 12 × 2.54 cm = 30.48 cm = 0.3048 m
Then:
600 ft² = (0.3048 m)² × 600
= 0.09290304 m² × 600 ≈ 55.74 m²
Method 3: Use Derived Conversion Factor
From method 2, we can store:
1 ft² = 0.09290304 m²
So:
600 × 0.09290304 ≈ 55.74 m²
Final Answer: The classroom area is approximately 55.7 m²
This value reflects the precision of the original data (600 ft²), which has 2–3 significant digits, so our answer is rounded accordingly.
