12.5g of a substance occupies `1.5 cm^(3)`. Express its density by keeping the significant figures in view.

Options

A. `8.3 g cm^(-3)`
B. `8.33 g cm^(-3)`
C. `8.333 g cm^(-3)`
D. `8.2 g cm^(-3)`

Answer

To find the density of the substance, we will follow these steps:

### Step 1: Identify the given values
- Mass (m) = 12.5 g
- Volume (V) = 1.5 cm³

### Step 2: Use the formula for density
The formula for density (ρ) is given by:
\[ \rho = \frac{m}{V} \]

### Step 3: Substitute the values into the formula
Substituting the values of mass and volume into the formula:
\[ \rho = \frac{12.5 \, \text{g}}{1.5 \, \text{cm}^3} \]

### Step 4: Perform the division
Now, let's perform the division:
\[ \rho = \frac{12.5}{1.5} \approx 8.3333 \, \text{g/cm}^3 \]

### Step 5: Determine significant figures
Next, we need to consider the significant figures.
- The mass (12.5 g) has **3 significant figures**.
- The volume (1.5 cm³) has **2 significant figures**.

Since the final answer must be reported with the least number of significant figures from the values used in the calculation, we will round our answer to **2 significant figures**.

### Step 6: Round the answer
The value 8.3333 rounded to 2 significant figures is:
- The first two digits are 8 and 3.
- The next digit (3) is less than 5, so we do not round up.

Thus, the density is:
\[ \rho = 8.3 \, \text{g/cm}^3 \]

### Final Answer
The density of the substance is **8.3 g/cm³**.

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