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 will 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
The formula for density (ρ) is given by:
\[ \rho = \frac{m}{V} \]
where:
- ρ = density
- m = mass
- V = volume

### 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 division
Calculating the density:
\[ \rho = 3.488 \, \text{g/cm}^3 \]

### Step 5: Determine the significant figures
Next, we need to round the result to the correct number of significant figures.

- The mass (87.2 g) has **3 significant figures** (the digits 8, 7, and 2).
- The volume (25 cm³) has **2 significant figures** (the digits 2 and 5).

The final result should be reported with the least number of significant figures from the values used in the calculation, which is **2 significant figures**.

### Step 6: Round the density to the correct significant figures
The calculated density is 3.488 g/cm³. To round this to 2 significant figures:
- The first two significant figures are 3 and 4.
- The next digit (8) is greater than 5, so we round up the second significant figure (4) to 5.

Thus, the density rounded to 2 significant figures is:
\[ \rho = 3.5 \, \text{g/cm}^3 \]

### Final Answer
The density of the block is **3.5 g/cm³**.

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