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Answer :
To determine the solution to the problem [tex]\( \frac{120}{7.11} \)[/tex] while expressing the answer to the correct number of significant figures, follow these steps:
1. Perform the Division:
- When you divide 120 by 7.11, the result is approximately 16.877637130801688.
2. Determine Significant Figures:
- The number 120 has two significant figures because we presume it is exact in front of the decimal and no additional information is provided about trailing zeros.
- The number 7.11 has three significant figures.
3. Apply Significant Figures Rule:
- The rule for division is that the result should be rounded to the same number of significant figures as the measurement with the least significant figures.
- Therefore, since 120 has two significant figures, we should round the answer to two significant figures.
4. Round the Result:
- The number 16.877637130801688 rounded to two significant figures is 17, because we look at the first two digits (16) and consider the next digit (8) for rounding.
5. Select the Correct Answer:
- Considering the choices:
A. 1.688
B. 1.69
C. 1.7
D. 1.70
- The properly rounded result, 17, is closest to option C, 1.7, when considering only two significant figures without additional specifications on decimal precision.
Thus, the correct answer to the problem, rounded to the correct number of significant figures, is option C: 1.7. However, I notice a discrepancy in choices with the real result, which means re-evaluation of the choices might be needed if more context about significant digits or representation was initially implied.
1. Perform the Division:
- When you divide 120 by 7.11, the result is approximately 16.877637130801688.
2. Determine Significant Figures:
- The number 120 has two significant figures because we presume it is exact in front of the decimal and no additional information is provided about trailing zeros.
- The number 7.11 has three significant figures.
3. Apply Significant Figures Rule:
- The rule for division is that the result should be rounded to the same number of significant figures as the measurement with the least significant figures.
- Therefore, since 120 has two significant figures, we should round the answer to two significant figures.
4. Round the Result:
- The number 16.877637130801688 rounded to two significant figures is 17, because we look at the first two digits (16) and consider the next digit (8) for rounding.
5. Select the Correct Answer:
- Considering the choices:
A. 1.688
B. 1.69
C. 1.7
D. 1.70
- The properly rounded result, 17, is closest to option C, 1.7, when considering only two significant figures without additional specifications on decimal precision.
Thus, the correct answer to the problem, rounded to the correct number of significant figures, is option C: 1.7. However, I notice a discrepancy in choices with the real result, which means re-evaluation of the choices might be needed if more context about significant digits or representation was initially implied.
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