To determine the sum of these masses with the appropriate number of significant figures, follow these detailed steps:
1. Identify the Given Masses:
- Mass 1: [tex]\( 15.673 \, \text{g} \)[/tex]
- Mass 2: [tex]\( 8.4568 \, \text{g} \)[/tex]
- Mass 3: [tex]\( 14.75 \, \text{g} \)[/tex]
2. Add the Masses Together:
[tex]\[
15.673 \, \text{g} + 8.4568 \, \text{g} + 14.75 \, \text{g} = 38.8798 \, \text{g}
\][/tex]
3. Determine the Number of Decimal Places for the Result:
The least precise measurement (the one with the least number of decimal places) dictates the number of decimal places in the final result. Here, the measurements have the following decimal places:
- Mass 1: 3 decimal places (15.673)
- Mass 2: 4 decimal places (8.4568)
- Mass 3: 2 decimal places (14.75)
Since the least number of decimal places is 2 (from 14.75 g), the final sum should be rounded to 2 decimal places.
4. Round the Sum to the Appropriate Number of Decimal Places:
[tex]\[
38.8798 \, \text{g} \approx 38.88 \, \text{g}
\][/tex]
5. Report the Final Sum:
The sum of the masses, reported to the appropriate number of significant figures, is:
[tex]\[
\boxed{38.88 \, \text{g}}
\][/tex]
Therefore, when the masses are added together and rounded to the least number of decimal places, the sum is [tex]\( 38.88 \, \text{g} \)[/tex].
