College

Select the answer with the correct number of significant figures for the calculation:

[tex]$31.580 + 4.26 =$[/tex]

A. 35.8
B. 35.84
C. 35.840

Answer :

Let's solve the problem of finding the correct number of significant figures in the calculation [tex]\(31.580 + 4.26\)[/tex].

1. Identify the Number of Significant Figures:
- [tex]\(31.580\)[/tex] has 5 significant figures.
- [tex]\(4.26\)[/tex] has 3 significant figures.

2. Addition Rule for Significant Figures:
- When adding or subtracting numbers, the answer should have the same number of decimal places as the number with the fewest decimal places.

3. Perform the Addition:
- Adding the two numbers, [tex]\(31.580 + 4.26\)[/tex], gives us an intermediate result of [tex]\(35.84\)[/tex].

4. Determine Decimal Places:
- Here, [tex]\(31.580\)[/tex] goes to three decimal places, but [tex]\(4.26\)[/tex] goes to two decimal places. So we round the answer to two decimal places.

5. Write the Final Answer:
- Therefore, the result with the correct number of significant figures is [tex]\(35.84\)[/tex].

Thus, the correct answer from the given options is [tex]\(35.84\)[/tex].