Answer :
Sure, let's solve this step-by-step.
### Step 1: Understand the Problem
You are given a mass of 103.8 grams and a volume of 2.23 cubic centimeters. You need to find the density and express your answer with the correct number of significant figures.
### Step 2: Perform the Calculation
First, you calculate the density using the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{103.8 \, \text{g}}{2.23 \, \text{cm}^3} \][/tex]
When you perform this division:
[tex]\[ \text{Density} \approx 46.547 \, \text{g/cm}^3 \][/tex]
### Step 3: Determine Significant Figures
To determine the significant figures for the final answer, you need to consider the significant figures in the given values:
- 103.8 grams has 4 significant figures.
- 2.23 cubic centimeters has 3 significant figures.
### Step 4: Apply the Rule of Significant Figures
In division (or multiplication), the result should have the same number of significant figures as the quantity with the fewest significant figures. Here, the limiting term is the volume, which has 3 significant figures.
### Step 5: Round the Result
The calculated density (46.547) should be rounded to 3 significant figures:
- Look at the fourth figure after the decimal (which is 7).
- Since it is 5 or greater, you round up the third figure (4) to 5.
Thus, the rounded density is:
[tex]\[ 46.5 \, \text{g/cm}^3 \][/tex]
### Conclusion
The correct choice from the given options is:
[tex]\[ 46.5 \, \text{g/cm}^3, \text{ the answer is limited to the total significant figures of the limiting term} \][/tex]
### Step 1: Understand the Problem
You are given a mass of 103.8 grams and a volume of 2.23 cubic centimeters. You need to find the density and express your answer with the correct number of significant figures.
### Step 2: Perform the Calculation
First, you calculate the density using the formula:
[tex]\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{103.8 \, \text{g}}{2.23 \, \text{cm}^3} \][/tex]
When you perform this division:
[tex]\[ \text{Density} \approx 46.547 \, \text{g/cm}^3 \][/tex]
### Step 3: Determine Significant Figures
To determine the significant figures for the final answer, you need to consider the significant figures in the given values:
- 103.8 grams has 4 significant figures.
- 2.23 cubic centimeters has 3 significant figures.
### Step 4: Apply the Rule of Significant Figures
In division (or multiplication), the result should have the same number of significant figures as the quantity with the fewest significant figures. Here, the limiting term is the volume, which has 3 significant figures.
### Step 5: Round the Result
The calculated density (46.547) should be rounded to 3 significant figures:
- Look at the fourth figure after the decimal (which is 7).
- Since it is 5 or greater, you round up the third figure (4) to 5.
Thus, the rounded density is:
[tex]\[ 46.5 \, \text{g/cm}^3 \][/tex]
### Conclusion
The correct choice from the given options is:
[tex]\[ 46.5 \, \text{g/cm}^3, \text{ the answer is limited to the total significant figures of the limiting term} \][/tex]