To solve the problem of adding [tex]\(12.77\)[/tex] and [tex]\(0.8\)[/tex] and rounding the result to the correct number of significant figures, let's follow these steps:
1. Determine the initial amounts: We are given two numbers:
[tex]\[
12.77 \quad \text{and} \quad 0.8
\][/tex]
2. Add the two numbers:
[tex]\[
12.77 + 0.8 = 13.57
\][/tex]
3. Consider the significant figures:
- [tex]\(12.77\)[/tex] has 4 significant figures.
- [tex]\(0.8\)[/tex] has 2 significant figures.
When adding or subtracting numbers, the result should be rounded to the least significant place of the numbers being added. In this case, [tex]\(0.8\)[/tex] has its least significant figure in the tenths place.
4. Round the result to the tenths place:
[tex]\[
13.57 \quad \text{rounded to the tenths place is} \quad 13.6
\][/tex]
5. Identify the correct answer:
Among the options provided, the one that corresponds to 13.6 is B.
So, the correct answer is:
[tex]\[
\boxed{13.6 \, \text{(Choice B)}}
\][/tex]
