calculate (3.1440 g - 0.084 g)/4.5132 cm3 with the correct number of significant figures

First, let's calculate the expression:

\[
\frac{(3.1440 \, \text{g} - 0.084 \, \text{g})}{4.5132 \, \text{cm}^3}
\]

### Step 1: Subtract the masses
\[
3.1440 \, \text{g} - 0.084 \, \text{g} = 3.0600 \, \text{g}
\]
Here, the result has 5 significant figures, which is determined by the number of decimal places in the original numbers (the least number is 3 decimal places, from 3.1440).

### Step 2: Perform the division
\[
\frac{3.0600 \, \text{g}}{4.5132 \, \text{cm}^3} \approx 0.67811 \, \text{g/cm}^3
\]

### Step 3: Apply significant figures
The number with the least significant figures in the division is 4.5132, which has 5 significant figures. Therefore, the result should be rounded to **5 significant figures**.

Thus, the final result is:
\[
\boxed{0.67811 \, \text{g/cm}^3}
\]

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How are significant figures determined in subtraction and division operations?
2. Why is the number of significant figures important in scientific calculations?
3. What are the rules for rounding when dealing with significant figures?
4. How would the result change if the mass values had different numbers of decimal places?
5. How do significant figures affect precision in experimental data?

**Tip:** Always apply the significant figure rules *after* performing each step in a multi-step calculation.

Learn how to solve (3.1440 g - 0.084 g) / 4.5132 cm³, applying the correct rules of significant figures. This detailed solution covers subtraction, division, and significant figure rounding, making it ideal for high school students in Grades 9-12.

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