An alleged gold nugget displaces 21 cm3 of water and has a mass of 371 grams. 

What is the density of this nugget ( in grams per mL ) to the correct number of significant figures ?

Report only the numerical value of this density in g/ mL units − do not enter units into the answer box. 

To calculate the density of the nugget and report it to the correct number of significant figures, follow these steps:

1. **Density formula**:
   \[
   \text{Density} = \frac{\text{Mass}}{\text{Volume}}
   \]
   where:
   - Mass \( = 371 \, \text{g} \)
   - Volume \( = 21 \, \text{cm}^3 \) (Note: 1 cm\(^3\) = 1 mL)

2. **Calculate the density**:
   \[
   \text{Density} = \frac{371 \, \text{g}}{21 \, \text{cm}^3} \approx 17.6667 \, \text{g/mL}
   \]

3. **Determine the correct number of significant figures**:
   - The mass \(371 \, \text{g}\) has 3 significant figures.
   - The volume \(21 \, \text{cm}^3\) has 2 significant figures.

   Since the volume has the least number of significant figures (2), the density should be reported with 2 significant figures.

4. **Round the result to 2 significant figures**:
   \[
   17.6667 \approx 18
   \]

**Final Answer**: 18

Would you like more details on this process or have any questions?

Here are 5 related questions for further exploration:
1. How would you calculate the density if the volume was given in liters?
2. What is the significance of using significant figures in scientific calculations?
3. Can you explain how to convert between different units of density?
4. How would a change in mass affect the density of an object if the volume remains constant?
5. What would be the density if the mass was 400 grams with the same volume?

**Tip**: When reporting a calculated value, always consider the number of significant figures based on the precision of the given measurements.

Learn how to calculate the density of a gold nugget displacing 21 cm³ of water with a mass of 371 grams. Understand the importance of significant figures in scientific calculations and the units of measurement involved. Discover the precise density in grams per milliliter (g/mL).

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