To determine the total mass of the three samples of granite and report it to the appropriate number of significant figures, follow these steps:
1. List the masses of the samples:
- Sample 1: [tex]\( 67.4 \, \text{g} \)[/tex]
- Sample 2: [tex]\( 43.2 \, \text{g} \)[/tex]
- Sample 3: [tex]\( 27.3 \, \text{g} \)[/tex]
2. Add the masses together to find the total mass:
[tex]\[
67.4 \, \text{g} + 43.2 \, \text{g} + 27.3 \, \text{g}
\][/tex]
3. Perform the addition:
[tex]\[
67.4 + 43.2 + 27.3 = 137.9 \, \text{g}
\][/tex]
4. Determine the appropriate number of significant figures:
- Each of the measured masses (67.4 g, 43.2 g, and 27.3 g) has 3 significant figures.
- When adding quantities, the result should be reported to the least number of decimal places in the addends.
- Each sample mass is given to one decimal place.
5. Adjust the total mass to the appropriate number of significant figures:
- The total mass when added up is 137.9 g.
- Since we are reporting to one decimal place (the least number of decimal places from our measurements), 137.9 g is already in the correct form with the correct number of significant figures.
Therefore, the total mass of the three samples, reported to the appropriate number of significant figures, is:
[tex]\[
137.9 \, \text{g}
\][/tex]
