Find density when a mass of 9.23 kg occupies a volume of `1.1m^3`. Take care of significant figures.

Explanation

To find the density when a mass of 9.23 kg occupies a volume of 1.1 m³, we can follow these steps:

### Step 1: Write the formula for density
The formula for density (ρ) is given by:
\[ \rho = \frac{\text{mass}}{\text{volume}} \]

### Step 2: Identify the given values
From the question, we have:
- Mass (m) = 9.23 kg
- Volume (V) = 1.1 m³

### Step 3: Substitute the values into the formula
Now we can substitute the values into the density formula:
\[ \rho = \frac{9.23 \, \text{kg}}{1.1 \, \text{m}^3} \]

### Step 4: Perform the division
Calculating the density:
\[ \rho = 9.23 \div 1.1 = 8.39090909 \ldots \, \text{kg/m}^3 \]

### Step 5: Determine the significant figures
Next, we need to consider significant figures. The number of significant figures in the values provided are:
- Mass (9.23 kg) has 3 significant figures.
- Volume (1.1 m³) has 2 significant figures.

### Step 6: Round the result to the appropriate significant figures
The final result should have the same number of significant figures as the measurement with the least significant figures, which is 2 in this case (from the volume).

The calculated density is approximately 8.39090909 kg/m³. Rounding this to 2 significant figures:
- The first two significant figures are 8.3. The next digit is 9, which is greater than 5, so we round up:
\[ \text{Rounded density} = 8.4 \, \text{kg/m}^3 \]

### Final Answer
The density is:
\[ \boxed{8.4 \, \text{kg/m}^3} \]

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