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Sagot :
Sure, let's analyze the significant figures for each given expression.
### Expression A: [tex]\(1001 + 47.41\)[/tex]
To determine the number of significant figures in the result, we add the numbers:
- [tex]\(1001\)[/tex] has 4 significant figures as the zeros are between significant digits.
- [tex]\(47.41\)[/tex] has 4 significant figures.
When adding/subtracting, the result should be rounded to the least number of decimal places present in the numbers. Since [tex]\(1001\)[/tex] has no decimal places and [tex]\(47.41\)[/tex] has two decimal places, the resulting sum will have no decimal places but retains 4 significant figures.
### Expression B: [tex]\(10.08 \cdot 4.731\)[/tex]
For multiplication, we consider the number of significant figures of each operand:
- [tex]\(10.08\)[/tex] has 4 significant figures.
- [tex]\(4.731\)[/tex] has 4 significant figures.
The result of a multiplication’s significant figures is determined by the operand with the least number of significant figures. Here, the product will have 4 significant figures.
### Expression C: [tex]\(4.67 + 14.3\)[/tex]
In adding these numbers, we count the significant figures and decimal places:
- [tex]\(4.67\)[/tex] has 3 significant figures.
- [tex]\(14.3\)[/tex] has 3 significant figures.
The result is rounded to the least number of decimal places. The number with the fewest decimal places is [tex]\(14.3\)[/tex] with one decimal place. The sum will have one decimal place, but still, both numbers contribute to the significant figures properly.
### Expression D: [tex]\(2011 \cdot 3.52\)[/tex]
For this multiplication:
- [tex]\(2011\)[/tex] has 4 significant figures.
- [tex]\(3.52\)[/tex] has 3 significant figures.
The product will be rounded to the least number of significant figures, which in this case is 3.
Based on the significant figure analysis for each expression:
- Expression A results in a number with more than 3 significant figures.
- Expression B results in a number with more than 3 significant figures.
- Expression C results in a sum with more than 3 significant figures.
- Expression D results in a product with more than 3 significant figures.
Thus, each expression correctly produces a result with more than 3 significant figures.
Therefore, the final answer is:
[tex]\[ \boxed{A, B, C, D} \][/tex]
### Expression A: [tex]\(1001 + 47.41\)[/tex]
To determine the number of significant figures in the result, we add the numbers:
- [tex]\(1001\)[/tex] has 4 significant figures as the zeros are between significant digits.
- [tex]\(47.41\)[/tex] has 4 significant figures.
When adding/subtracting, the result should be rounded to the least number of decimal places present in the numbers. Since [tex]\(1001\)[/tex] has no decimal places and [tex]\(47.41\)[/tex] has two decimal places, the resulting sum will have no decimal places but retains 4 significant figures.
### Expression B: [tex]\(10.08 \cdot 4.731\)[/tex]
For multiplication, we consider the number of significant figures of each operand:
- [tex]\(10.08\)[/tex] has 4 significant figures.
- [tex]\(4.731\)[/tex] has 4 significant figures.
The result of a multiplication’s significant figures is determined by the operand with the least number of significant figures. Here, the product will have 4 significant figures.
### Expression C: [tex]\(4.67 + 14.3\)[/tex]
In adding these numbers, we count the significant figures and decimal places:
- [tex]\(4.67\)[/tex] has 3 significant figures.
- [tex]\(14.3\)[/tex] has 3 significant figures.
The result is rounded to the least number of decimal places. The number with the fewest decimal places is [tex]\(14.3\)[/tex] with one decimal place. The sum will have one decimal place, but still, both numbers contribute to the significant figures properly.
### Expression D: [tex]\(2011 \cdot 3.52\)[/tex]
For this multiplication:
- [tex]\(2011\)[/tex] has 4 significant figures.
- [tex]\(3.52\)[/tex] has 3 significant figures.
The product will be rounded to the least number of significant figures, which in this case is 3.
Based on the significant figure analysis for each expression:
- Expression A results in a number with more than 3 significant figures.
- Expression B results in a number with more than 3 significant figures.
- Expression C results in a sum with more than 3 significant figures.
- Expression D results in a product with more than 3 significant figures.
Thus, each expression correctly produces a result with more than 3 significant figures.
Therefore, the final answer is:
[tex]\[ \boxed{A, B, C, D} \][/tex]
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