To find the sum of the masses of the three samples of chalk, we need to consider both the actual summation and the appropriate number of significant figures for the final result. Here's a step-by-step explanation:
1. List the Masses:
- Mass of the first sample: [tex]\(15.673 \, \text{g}\)[/tex]
- Mass of the second sample: [tex]\(8.4568 \, \text{g}\)[/tex]
- Mass of the third sample: [tex]\(14.75 \, \text{g}\)[/tex]
2. Sum the Masses:
To find the total mass, simply add the three masses together:
[tex]\[
15.673 + 8.4568 + 14.75 = 38.8798 \, \text{g}
\][/tex]
3. Determine the Number of Decimal Places:
The rule for addition and subtraction with significant figures is that the result should have the same number of decimal places as the measurement with the fewest decimal places.
- [tex]\(15.673\)[/tex] has 3 decimal places.
- [tex]\(8.4568\)[/tex] has 4 decimal places.
- [tex]\(14.75\)[/tex] has 2 decimal places (this is the minimum number of decimal places).
4. Round the Result:
Since the smallest number of decimal places among the given masses is 2, the final result should be rounded to 2 decimal places. Therefore, we round [tex]\(38.8798 \, \text{g}\)[/tex] to 2 decimal places:
[tex]\[
38.8798 \approx 38.88
\][/tex]
5. Final Answer:
The sum of the masses, reported to the appropriate number of significant figures, is [tex]\(38.88 \, \text{g}\)[/tex].
