The mass of `1.2cm^(3)` of a certain substance is 5.74 g. Its density with due regard to significant figure is

Options

A. `4.7gcm^(-3)`
B. `4.8gcm^(-3)`
C. `4.5gcm^(-3)`
D. `4.6gcm^(-3)`

Explanation

To find the density of the substance with the given mass and volume, we will follow these steps:

### Step 1: Identify the given values
- Mass of the substance = 5.74 g
- Volume of the substance = 1.2 cm³

### Step 2: Determine the number of significant figures
- The mass (5.74 g) has 3 significant figures.
- The volume (1.2 cm³) has 2 significant figures.

### Step 3: Calculate the density
Density is defined as mass per unit volume. Therefore, we can calculate the density using the formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Substituting the values:

\[ \text{Density} = \frac{5.74 \, \text{g}}{1.2 \, \text{cm}^3} \]

### Step 4: Perform the division
Calculating the density:

\[ \text{Density} = 4.7833 \, \text{g/cm}^3 \]

### Step 5: Apply the rules of significant figures
Since we are dividing, the result should have the same number of significant figures as the value with the least significant figures. In this case, the volume (1.2 cm³) has 2 significant figures.

### Step 6: Round the result to the appropriate number of significant figures
We need to round 4.7833 to 2 significant figures. The first two significant figures are 4 and 7. The next digit is 8, which is greater than 5, so we round up:

\[ \text{Rounded Density} = 4.8 \, \text{g/cm}^3 \]

### Final Answer
The density of the substance, with due regard to significant figures, is **4.8 g/cm³**.

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