A sheet of metal (of constant thickness) has a density of 238 grams per square meter. What is this density in ounces per square inch? Note that there are exactly 2.54 cm in 1 inch, exactly 12 inches in 1 foot, exactly 16 ounces in a pound, and 2.205 pounds in a kilogram (to 4 significant figures). Write your answer with or without scientific notation. If using scientific notation, note that 0.02574 would be written as 2.574e-2.
The Correct Answer and Explanation is:
We are tasked with converting a density of 238 grams per square meter into ounces per square inch.
Step 1: Convert grams to ounces.
First, we need to convert grams into ounces. The conversion factor is: 1 ounce=28.3495 grams1 \text{ ounce} = 28.3495 \text{ grams}1 ounce=28.3495 grams
So, to convert 238 grams to ounces: 238 grams×1 ounce28.3495 grams=8.399 ounces238 \, \text{grams} \times \frac{1 \, \text{ounce}}{28.3495 \, \text{grams}} = 8.399 \, \text{ounces}238grams×28.3495grams1ounce=8.399ounces
Step 2: Convert square meters to square inches.
Next, we convert square meters to square inches. The conversion factor between meters and inches is: 1 inch=2.54 cm1 \, \text{inch} = 2.54 \, \text{cm}1inch=2.54cm
Since 1 meter = 100 cm, we have: 1 meter=1002.54 inches=39.3701 inches1 \, \text{meter} = \frac{100}{2.54} \, \text{inches} = 39.3701 \, \text{inches}1meter=2.54100inches=39.3701inches
So, 1 square meter is: 1 m2=(39.3701)2 inches2=1550.0031 inches21 \, \text{m}^2 = (39.3701)^2 \, \text{inches}^2 = 1550.0031 \, \text{inches}^21m2=(39.3701)2inches2=1550.0031inches2
Step 3: Combine the conversions.
Now, we have: Density in ounces per square inch=8.399 ounces1550.0031 inches2\text{Density in ounces per square inch} = \frac{8.399 \, \text{ounces}}{1550.0031 \, \text{inches}^2}Density in ounces per square inch=1550.0031inches28.399ounces
Performing the division: 8.3991550.0031≈0.005414 ounces per square inch\frac{8.399}{1550.0031} \approx 0.005414 \, \text{ounces per square inch}1550.00318.399≈0.005414ounces per square inch
Final Answer:
The density is approximately 0.005414 ounces per square inch.
Explanation:
To arrive at this answer, we converted the given density from grams per square meter to ounces per square inch by first converting the mass (grams to ounces) and then converting the area (square meters to square inches). The result, 0.005414, is a density measure that expresses the mass in ounces for each square inch of the metal sheet.
