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 in correct significant figures, we will follow these steps:

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

### Step 4: Perform the calculation
Calculating the density:
\[ \rho = \frac{4.237}{2.5} = 1.6948 \, \text{g/cm}^3 \]

### Step 5: Determine the significant figures
Now we need to express the density in the correct number of significant figures. The mass (4.237 g) has 4 significant figures, while the volume (2.5 cm³) has 2 significant figures.

According to the rules of significant figures in multiplication and division, the result should have the same number of significant figures as the measurement with the least significant figures. Here, that is 2 significant figures (from the volume).

### Step 6: Round the result
Rounding 1.6948 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.
- Therefore, 1.6948 rounded to 2 significant figures is 1.7.

### Step 7: Write the final answer
Thus, the density of the material of the body in correct significant figures is:
\[ \rho = 1.7 \, \text{g/cm}^3 \]

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