High School

Using Significant Figures for Calculation

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 :

Sure, let's solve this step-by-step considering significant figures:

1. Understanding the Issue of Significant Figures: Significant figures are the digits in a number that carry meaning contributing to its precision. This includes all digits except:
- Leading zeros
- Trailing zeros when they serve as placeholders to indicate the scale of the number (depending on if there's a decimal point)
- Spurious digits introduced, for example, by calculations carried out to more precision than that of the original data.

2. Performing the Addition:
- We have the numbers 31.580 and 4.26 to be added.

3. Identify the Number of Decimal Places:
- 31.580 has three decimal places.
- 4.26 has two decimal places.

4. Determining the Number of Decimal Places in the Result:
- When adding or subtracting numbers, the result should have the same number of decimal places as the measurement with the least number of decimal places.
- Here, 4.26 has the least number with two decimal places.

5. Calculating the Sum:
- Add the numbers:
[tex]\[
31.580 + 4.26 = 35.840
\][/tex]

6. Rounding the Result:
- We need to round 35.840 to two decimal places (since 4.26 has two decimal places).
- Rounding 35.840 to two decimal places gives us 35.84.

7. Adjust for Significant Figures:
- Although the sum is calculated with two decimal places, the result should consider the overall significant figures from the input data, resulting in three significant figures.
- Therefore, the result rounded to three significant figures, considering the impact of precision, is 35.8.

So, the final answer with the correct number of significant figures is 35.8.