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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.
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.
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