The mass and volume of a body are 4.237 g and `2.5cm^(3)` respectively. The density of the material of the body in correct significant figures is

Options

A. `1.6048" g"" cm"^(-3)`
B. `1.69" g"" cm"^(-3)`
C. `1.7" g"" cm"^(-3)`
D. `1.695" g"" cm"^(-3)`

Explanation

To find the density of the material of the body given its mass and volume, we will follow these steps:

### Step 1: Identify the given values
- Mass of the body \( m = 4.237 \, \text{g} \)
- Volume of the body \( V = 2.5 \, \text{cm}^3 \)

### Step 2: Calculate the density
Density (\( \rho \)) is defined as mass per unit volume. The formula for density is:
\[ \rho = \frac{m}{V} \]
Substituting the given values:
\[ \rho = \frac{4.237 \, \text{g}}{2.5 \, \text{cm}^3} \]

### Step 3: Perform the division
Calculating the above expression:
\[ \rho = 1.6948 \, \text{g/cm}^3 \]

### Step 4: Determine significant figures
- The mass \( 4.237 \, \text{g} \) has **4 significant figures**.
- The volume \( 2.5 \, \text{cm}^3 \) has **2 significant figures**.

When performing calculations, the result should have the same number of significant figures as the measurement with the least significant figures. Here, the volume has the least significant figures (2).

### Step 5: Round the result to the correct significant figures
The calculated density \( 1.6948 \, \text{g/cm}^3 \) has 5 significant figures. We need to round it to 2 significant figures:
- The first two significant figures are **1** and **6**.
- The next digit is **9**, which is greater than 5, so we round up the second significant figure from **6** to **7**.

Thus, the density rounded to 2 significant figures is:
\[ \rho \approx 1.7 \, \text{g/cm}^3 \]

### Final Answer
The density of the material of the body in correct significant figures is:
\[ \boxed{1.7 \, \text{g/cm}^3} \]