The mass of a block is 87.2 g and its volume is `25 cm^(3)`. What is its density up to correct significant figures?

Answer

To find the density of the block, we can follow these steps:

### Step 1: Identify the given values
- Mass of the block (m) = 87.2 g
- Volume of the block (V) = 25 cm³

### Step 2: Use the formula for density
Density (ρ) is calculated using the formula:
\[ \rho = \frac{m}{V} \]

### Step 3: Substitute the values into the formula
Substituting the given values into the density formula:
\[ \rho = \frac{87.2 \, \text{g}}{25 \, \text{cm}^3} \]

### Step 4: Perform the calculation
Calculating the density:
\[ \rho = \frac{87.2}{25} = 3.488 \, \text{g/cm}^3 \]

### Step 5: Determine the significant figures
- The mass (87.2 g) has 3 significant figures.
- The volume (25 cm³) has 2 significant figures.
- The density must be reported with the minimum number of significant figures from the measurements used, which is 2 significant figures (from the volume).

### Step 6: Round the result to the correct significant figures
The calculated density is 3.488 g/cm³. To round this to 2 significant figures:
- Look at the third significant figure (8). Since it is greater than 5, we round up the second significant figure (4) by 1.

Thus, 3.488 rounded to 2 significant figures is 3.5 g/cm³.

### Final Answer
The density of the block is:
\[ \rho = 3.5 \, \text{g/cm}^3 \]

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