To determine the level of precision for the solution to the addition problem, we need to look at the number of decimal places in each of the measurements. Here are the measurements given:
1. [tex]\(6.339 \, \text{m}\)[/tex]: This number has 3 decimal places.
2. [tex]\(0.170 \, \text{m}\)[/tex]: This number also has 3 decimal places.
3. [tex]\(30.4 \, \text{m}\)[/tex]: This number has 1 decimal place.
When adding numbers, the result should be rounded to the least number of decimal places found in the numbers being added. The measurement with the fewest decimal places is [tex]\(30.4 \, \text{m}\)[/tex], which has just 1 decimal place.
Therefore, the result of the addition should be rounded to 1 decimal place.
The addition of the measurements is:
[tex]\[
6.339 \, \text{m} + 0.170 \, \text{m} + 30.4 \, \text{m} = 36.909 \, \text{m}
\][/tex]
Rounding 36.909 to 1 decimal place, we get 36.9.
Hence, the level of precision for the solution to this addition problem is [tex]\(0.1 \, \text{m}\)[/tex] (since 1 decimal place corresponds to tenths or 0.1).
So, the answer is:
[tex]\[ \boxed{0.1 \, \text{m}} \][/tex]
