Answer :
- Divide 12.0 by 7.11, which equals approximately 1.68776.
- Determine the number of significant figures: both numbers have three significant figures.
- Round the result to three significant figures: 1.69.
- Select the correct option: $\boxed{1.69}$.
### Explanation
1. Understanding Significant Figures
We are asked to divide 12.0 by 7.11 and express the answer to the correct number of significant figures. The number 12.0 has three significant figures, and the number 7.11 also has three significant figures. When dividing, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, both numbers have three significant figures, so the answer should have three significant figures.
2. Performing the Division
Now, let's perform the division: $\frac{12.0}{7.11} = 1.6877637130801686$.
3. Rounding to Three Significant Figures
We need to round the result to three significant figures. The first three digits are 1.68, and the next digit is 7, which is greater than or equal to 5, so we round up the last digit. Therefore, 1.68 becomes 1.69.
4. Selecting the Correct Answer
Comparing our rounded result, 1.69, to the given options, we find that it matches option B.
### Examples
Significant figures are crucial in scientific calculations to accurately represent the precision of measurements. For instance, if you're calculating the density of a substance using mass and volume measurements, the density should be reported with the same number of significant figures as the least precise measurement. This ensures that the calculated result doesn't imply a higher level of precision than the original measurements allow. In practical fields like engineering and chemistry, using the correct number of significant figures prevents misinterpretations and errors in critical calculations.
- Determine the number of significant figures: both numbers have three significant figures.
- Round the result to three significant figures: 1.69.
- Select the correct option: $\boxed{1.69}$.
### Explanation
1. Understanding Significant Figures
We are asked to divide 12.0 by 7.11 and express the answer to the correct number of significant figures. The number 12.0 has three significant figures, and the number 7.11 also has three significant figures. When dividing, the result should have the same number of significant figures as the number with the fewest significant figures. In this case, both numbers have three significant figures, so the answer should have three significant figures.
2. Performing the Division
Now, let's perform the division: $\frac{12.0}{7.11} = 1.6877637130801686$.
3. Rounding to Three Significant Figures
We need to round the result to three significant figures. The first three digits are 1.68, and the next digit is 7, which is greater than or equal to 5, so we round up the last digit. Therefore, 1.68 becomes 1.69.
4. Selecting the Correct Answer
Comparing our rounded result, 1.69, to the given options, we find that it matches option B.
### Examples
Significant figures are crucial in scientific calculations to accurately represent the precision of measurements. For instance, if you're calculating the density of a substance using mass and volume measurements, the density should be reported with the same number of significant figures as the least precise measurement. This ensures that the calculated result doesn't imply a higher level of precision than the original measurements allow. In practical fields like engineering and chemistry, using the correct number of significant figures prevents misinterpretations and errors in critical calculations.
