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Answer :
Sure! Let's go through the problem step-by-step and determine the correct number of significant figures for each calculation.
1. Addition: [tex]\(31.580 + 4.26\)[/tex]
- When adding numbers, the result should have the same number of decimal places as the number with the least decimal places.
- Here, 31.580 has three decimal places and 4.26 has two decimal places.
- So, the result should be rounded to two decimal places.
- Calculation: [tex]\(31.580 + 4.26 = 35.84\)[/tex]
- Final Answer: 35.84
2. Subtraction: [tex]\(1.0250 - 0.00063\)[/tex]
- When subtracting numbers, the result should have the same number of decimal places as the number with the least decimal places.
- Here, 1.0250 has four decimal places and 0.00063 has five decimal places.
- But because of the leading zeroes, we focus on their significant figures. The subtraction is typically done according to significant figures in the context of decimal places rather than significant digits.
- As this doesn't apply directly here, both have enough decimal precision.
- Calculation: [tex]\(1.0250 - 0.00063 = 1.02437\)[/tex]
- Final Answer: 1.02437
3. Multiplication: [tex]\(35.8 \times 1.02\)[/tex]
- For multiplication, the result should have the same number of significant figures as the number with the least significant figures.
- In this case, 35.8 has three significant figures and 1.02 also has three significant figures.
- So, the result should be rounded to three significant figures.
- Calculation: [tex]\(35.8 \times 1.02 = 36.516\)[/tex]
- Rounding to three significant figures gives us: 36.5
- Final Answer: 36.5
These are the correct number of significant figures and results for each calculation.
1. Addition: [tex]\(31.580 + 4.26\)[/tex]
- When adding numbers, the result should have the same number of decimal places as the number with the least decimal places.
- Here, 31.580 has three decimal places and 4.26 has two decimal places.
- So, the result should be rounded to two decimal places.
- Calculation: [tex]\(31.580 + 4.26 = 35.84\)[/tex]
- Final Answer: 35.84
2. Subtraction: [tex]\(1.0250 - 0.00063\)[/tex]
- When subtracting numbers, the result should have the same number of decimal places as the number with the least decimal places.
- Here, 1.0250 has four decimal places and 0.00063 has five decimal places.
- But because of the leading zeroes, we focus on their significant figures. The subtraction is typically done according to significant figures in the context of decimal places rather than significant digits.
- As this doesn't apply directly here, both have enough decimal precision.
- Calculation: [tex]\(1.0250 - 0.00063 = 1.02437\)[/tex]
- Final Answer: 1.02437
3. Multiplication: [tex]\(35.8 \times 1.02\)[/tex]
- For multiplication, the result should have the same number of significant figures as the number with the least significant figures.
- In this case, 35.8 has three significant figures and 1.02 also has three significant figures.
- So, the result should be rounded to three significant figures.
- Calculation: [tex]\(35.8 \times 1.02 = 36.516\)[/tex]
- Rounding to three significant figures gives us: 36.5
- Final Answer: 36.5
These are the correct number of significant figures and results for each calculation.
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