Let's solve this step by step to determine the level of precision for the solution.
1. Identify the measurements to be added:
- [tex]\(6.339 \, \text{m}\)[/tex]
- [tex]\(0.170 \, \text{m}\)[/tex]
- [tex]\(30.4 \, \text{m}\)[/tex]
2. Determine the precision of each measurement:
- [tex]\(6.339 \, \text{m}\)[/tex]: This measurement is precise to the nearest thousandth ([tex]\(0.001 \, \text{m}\)[/tex]).
- [tex]\(0.170 \, \text{m}\)[/tex]: This measurement is also precise to the nearest thousandth ([tex]\(0.001 \, \text{m}\)[/tex]).
- [tex]\(30.4 \, \text{m}\)[/tex]: This measurement is precise to the nearest tenth ([tex]\(0.1 \, \text{m}\)[/tex]).
3. Understand the rule for addition with significant figures:
When adding or subtracting measurements, the result should be rounded to the least precise decimal place of the numbers being added.
4. Identify the least precise measurement:
The least precise measurement is [tex]\(30.4 \, \text{m}\)[/tex], which is precise to the nearest tenth ([tex]\(0.1 \, \text{m}\)[/tex]).
5. Add the measurements (although not required, this step confirms the process):
- Adding, we get a total measurement of [tex]\(36.909 \, \text{m}\)[/tex].
6. Determine the level of precision:
According to the rule of significant figures in addition, the least precise measurement dictates the precision of the total.
Therefore, the total measurement [tex]\(36.909 \, \text{m}\)[/tex] needs to be rounded to the nearest tenth.
Hence, the level of precision for the solution to the addition problem is [tex]\(0.1 \, \text{m}\)[/tex].
