The mass of a metal block is 5.432 g. If density of metal is `6.4 g//cm^(3)`, what is its volume ? Express the result to the appropriate significant figures.

Answer

To find the volume of the metal block, we will use the formula for density, which relates mass, volume, and density:

**Step 1: Write down the formula for density.**
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
From this, we can rearrange the formula to solve for volume:
\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

**Step 2: Identify the given values.**
- Mass of the metal block = 5.432 g
- Density of the metal = 6.4 g/cm³

**Step 3: Substitute the values into the volume formula.**
\[ \text{Volume} = \frac{5.432 \, \text{g}}{6.4 \, \text{g/cm}^3} \]

**Step 4: Perform the calculation.**
\[ \text{Volume} = \frac{5.432}{6.4} \approx 0.84875 \, \text{cm}^3 \]

**Step 5: Round the result to the appropriate significant figures.**
- The mass (5.432 g) has 4 significant figures.
- The density (6.4 g/cm³) has 2 significant figures.
- Therefore, the volume should be expressed with 2 significant figures (the least number of significant figures from the given values).

When rounding 0.84875 to 2 significant figures, we look at the first two digits (84) and the next digit (8). Since 8 is greater than 5, we round up:
\[ \text{Rounded Volume} = 0.85 \, \text{cm}^3 \]

**Final Answer:**
The volume of the metal block is \(0.85 \, \text{cm}^3\).

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