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Answer :
To determine the solution of the division [tex]\(\frac{120}{111}\)[/tex] to the correct number of significant figures, we should follow these steps:
1. Perform the Division: First, divide 120 by 111 using a calculator. This gives a result of approximately 1.0810810810810811.
2. Identify Significant Figures: In significant figures, we need to compare the number of significant figures in both the numerator (120) and the denominator (111). The number with the fewest significant figures dictates the number of significant figures in the result.
- The number 120 has 2 significant figures (the 1 and the 2).
- The number 111 has 3 significant figures (the 1's in 111).
So, the result should be expressed with 2 significant figures because 120 has the fewest.
3. Round to Correct Number of Significant Figures: This means we should round 1.0810810810810811 to 2 significant figures. Doing that:
- Start with the first significant figure, which is '1'.
- The second significant figure is '0'.
- The next digit is '8', which is 5 or more, so we round the '0' up to '1'.
Therefore, rounding 1.0810810810810811 to 2 significant figures gives us 1.1.
None of the provided answers matches exactly with the calculation using 2 significant figures. As per the multiple-choice options, our calculation does not correctly match any proposed choice with 2 significant figures. However, typically, if you were to be rounding to 2 decimal places, the number of significant figures normally should be revisited.
However, since option B (1.69) or option C (1.7) seem to misunderstand the given result, based on factual calculation, sticking to significant figures analysis indicates a misunderstanding without further context on instructions preferences.
1. Perform the Division: First, divide 120 by 111 using a calculator. This gives a result of approximately 1.0810810810810811.
2. Identify Significant Figures: In significant figures, we need to compare the number of significant figures in both the numerator (120) and the denominator (111). The number with the fewest significant figures dictates the number of significant figures in the result.
- The number 120 has 2 significant figures (the 1 and the 2).
- The number 111 has 3 significant figures (the 1's in 111).
So, the result should be expressed with 2 significant figures because 120 has the fewest.
3. Round to Correct Number of Significant Figures: This means we should round 1.0810810810810811 to 2 significant figures. Doing that:
- Start with the first significant figure, which is '1'.
- The second significant figure is '0'.
- The next digit is '8', which is 5 or more, so we round the '0' up to '1'.
Therefore, rounding 1.0810810810810811 to 2 significant figures gives us 1.1.
None of the provided answers matches exactly with the calculation using 2 significant figures. As per the multiple-choice options, our calculation does not correctly match any proposed choice with 2 significant figures. However, typically, if you were to be rounding to 2 decimal places, the number of significant figures normally should be revisited.
However, since option B (1.69) or option C (1.7) seem to misunderstand the given result, based on factual calculation, sticking to significant figures analysis indicates a misunderstanding without further context on instructions preferences.
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