Final answer:
The density in g/mL, convert 0.897 pounds to grams and 13.5 cubic inches to milliliters, then divide the mass by the volume. After rounding, the density is 1.84 g/mL.
Step-by-step explanation:
To calculate the density in g/mL of an unknown substance where 0.897 pounds occupy 13.5 cubic inches, we must first convert pounds to grams and cubic inches to milliliters (mL).
The conversion factors are:
- 1 pound = 453.59237 grams
- 1 inch^3 = 16.387064 mL
First, convert the mass in pounds to grams:
0.897 pounds × 453.59237 g/pound = 406.87663629 grams
Next, convert the volume in cubic inches to milliliters:
13.5 inch^3 × 16.387064 mL/inch^3 = 221.225364 mL
Now, divide the mass by the volume to find the density:
406.87663629 grams / 221.225364 mL = 1.83909345 g/mL
To express this value with three significant figures, we round it to 1.84 g/mL.