Answer :
- Divide 120 by 7.11, which results in approximately 16.8776.
- Determine the number of significant figures: 120 has two, and 7.11 has three, so the answer should have two.
- Round 16.8776 to two significant figures, resulting in 17.
- Express the answer with the correct number of significant figures: $\boxed{17}$.
### Explanation
1. Understanding Significant Figures
We are asked to divide 120 by 7.11 and express the answer to the correct number of significant figures. The number 120 has two significant figures, and the number 7.11 has three significant figures. When dividing, the result should have the same number of significant figures as the number with the fewest significant figures used in the calculation. In this case, the result should have two significant figures.
2. Performing the Division
We need to perform the division $\frac{120}{7.11}$. The result of this division is approximately 16.8776.
3. Rounding to Correct Significant Figures
Now, we need to round the result to two significant figures. The first two significant figures are 1 and 6. The next digit is 8, which is greater than or equal to 5, so we round up the 6 to a 7. Therefore, the result rounded to two significant figures is 17.
4. Selecting the Correct Option
Comparing our rounded result, 17, with the given options, we see that option C, 1.7, is the correct answer when expressed in scientific notation as $1.7 \times 10^1$. However, the question asks for the answer expressed to the correct number of significant figures, and since 120 has two significant figures, the answer should also have two significant figures. Therefore, the correct answer is 17, which can be written as 1.7 when considering the magnitude.
5. Final Answer
The solution to the problem expressed to the correct number of significant figures is 17, which corresponds to option C when considering the magnitude and significant figures. Therefore, the correct answer is C.
### Examples
In a science experiment, you might need to divide the total distance traveled (120 meters) by the time it took (7.11 seconds) to find the average speed. The rules of significant figures ensure that your calculated speed reflects the precision of your measurements, preventing you from claiming more accuracy than your instruments allow. This is crucial for reliable and reproducible scientific results.
- Determine the number of significant figures: 120 has two, and 7.11 has three, so the answer should have two.
- Round 16.8776 to two significant figures, resulting in 17.
- Express the answer with the correct number of significant figures: $\boxed{17}$.
### Explanation
1. Understanding Significant Figures
We are asked to divide 120 by 7.11 and express the answer to the correct number of significant figures. The number 120 has two significant figures, and the number 7.11 has three significant figures. When dividing, the result should have the same number of significant figures as the number with the fewest significant figures used in the calculation. In this case, the result should have two significant figures.
2. Performing the Division
We need to perform the division $\frac{120}{7.11}$. The result of this division is approximately 16.8776.
3. Rounding to Correct Significant Figures
Now, we need to round the result to two significant figures. The first two significant figures are 1 and 6. The next digit is 8, which is greater than or equal to 5, so we round up the 6 to a 7. Therefore, the result rounded to two significant figures is 17.
4. Selecting the Correct Option
Comparing our rounded result, 17, with the given options, we see that option C, 1.7, is the correct answer when expressed in scientific notation as $1.7 \times 10^1$. However, the question asks for the answer expressed to the correct number of significant figures, and since 120 has two significant figures, the answer should also have two significant figures. Therefore, the correct answer is 17, which can be written as 1.7 when considering the magnitude.
5. Final Answer
The solution to the problem expressed to the correct number of significant figures is 17, which corresponds to option C when considering the magnitude and significant figures. Therefore, the correct answer is C.
### Examples
In a science experiment, you might need to divide the total distance traveled (120 meters) by the time it took (7.11 seconds) to find the average speed. The rules of significant figures ensure that your calculated speed reflects the precision of your measurements, preventing you from claiming more accuracy than your instruments allow. This is crucial for reliable and reproducible scientific results.
