the mass of piece of paper is 0.02 g and the mass of a solid substance along with the same piece of paper is 20.036 g. If the volume of the solid is `2.16cm^(3)`, its density to the proper number of significant digits will be

Options

A. `9.3gcm^(-3)`
B. `9.34gcm^(-3)`
C. `9.27gcm^(-3)`
D. `43.24cm^(-3)`

Explanation

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

### Step 1: Calculate the mass of the solid substance
To find the mass of the solid substance, we subtract the mass of the piece of paper from the total mass.

\[ \text{Mass of solid} = \text{Total mass} - \text{Mass of paper} \]
\[ \text{Mass of solid} = 20.036 \, \text{g} - 0.02 \, \text{g} = 20.016 \, \text{g} \]

### Step 2: Use the formula for density
Density is defined as mass per unit volume. The formula for density (D) is:

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

### Step 3: Substitute the values into the density formula
Now we can substitute the mass of the solid and its volume into the density formula.

\[ D = \frac{20.016 \, \text{g}}{2.16 \, \text{cm}^3} \]

### Step 4: Perform the calculation
Calculating the density gives:

\[ D = 9.26666667 \, \text{g/cm}^3 \]

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

- The mass of the solid (20.016 g) has **5 significant figures**.
- The volume (2.16 cm³) has **3 significant figures**.

The final answer should be reported with the least number of significant figures, which is **3 significant figures**.

### Step 6: Round the density
Rounding 9.26666667 to 3 significant figures:

- The first three digits are 9.26.
- The next digit is 6, which is greater than 5, so we round up.

Thus, the density rounded to 3 significant figures is:

\[ D = 9.27 \, \text{g/cm}^3 \]

### Final Answer
The density of the solid substance is **9.27 g/cm³**.

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