The density of a certain material is such that it weighs 18000 milligrams per milliliter of volume. Express this density in pounds per cup. Round your answer to the nearest hundredth.

To solve the problem of converting the density from milligrams per milliliter to pounds per cup, we'll follow these steps:

1. **Identify the given density**:
   \[
   \text{Density} = 18000 \, \text{mg/mL}
   \]

2. **Convert milligrams to pounds**:
   \[
   1 \, \text{mg} = 2.20462 \times 10^{-6} \, \text{pounds}
   \]
   So,
   \[
   18000 \, \text{mg} = 18000 \times 2.20462 \times 10^{-6} \, \text{pounds}
   \]

3. **Convert milliliters to cups**:
   \[
   1 \, \text{mL} = 0.00422675 \, \text{cups}
   \]

4. **Calculate the density in pounds per cup**:
   \[
   \text{Density in pounds per cup} = \frac{18000 \times 2.20462 \times 10^{-6} \, \text{pounds}}{0.00422675 \, \text{cups}}
   \]

Let's calculate that.The density of the material is approximately **9.39 pounds per cup**, rounded to the nearest hundredth.

Would you like more details or have any questions? Here are some related questions:

1. How would you convert density from pounds per cup to grams per liter?
2. What is the density in kilograms per cubic meter if the original density is 18000 mg/mL?
3. How do you convert cubic centimeters to cups, and how is it related to this problem?
4. What is the significance of using different units like milligrams, pounds, and cups in practical scenarios?
5. How would you approach converting density from pounds per cubic foot to kilograms per liter?
6. Why is it important to round off answers, and when should you avoid rounding?
7. How do changes in temperature affect the density of materials?
8. Can density be expressed as a ratio? If so, how?

**Tip**: When dealing with unit conversions, always ensure consistency by carefully tracking each unit throughout the calculation.

Learn how to convert density from milligrams per milliliter to pounds per cup with a step-by-step solution. Understand the unit conversions involved and calculate the density in pounds per cup. Suitable for high school students and above.

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