Answer :
- Divide 12.0 by 7.11: $\frac{12.0}{7.11} = 1.6877637130801686$.
- Determine the number of significant figures: Both 12.0 and 7.11 have three significant figures.
- Round the result to three significant figures: $1.6877637130801686 \approx 1.69$.
- The final answer is $\boxed{1.69}$.
### Explanation
1. Understanding the problem
We are asked to calculate the result of the division $\frac{12.0}{7.11}$ and express the answer to the correct number of significant figures.
2. 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 result should have three significant figures.
3. Performing the division
The result of the division is $\frac{12.0}{7.11} = 1.6877637130801686$. We need to round this result to three significant figures.
4. Rounding to correct number of significant figures
Rounding 1.6877637130801686 to three significant figures gives us 1.69.
5. Final Answer
Therefore, the solution to the problem expressed to the correct number of significant figures is 1.69.
### Examples
In a science experiment, you might need to divide the mass of a substance by its volume to find its density. If your measurements are 12.0 grams and 7.11 cubic centimeters, you would calculate the density as 12.0/7.11. Expressing the result with the correct number of significant figures (1.69 g/cm³) ensures your calculation reflects the precision of your measurements, preventing misleading conclusions about the substance's properties.
- Determine the number of significant figures: Both 12.0 and 7.11 have three significant figures.
- Round the result to three significant figures: $1.6877637130801686 \approx 1.69$.
- The final answer is $\boxed{1.69}$.
### Explanation
1. Understanding the problem
We are asked to calculate the result of the division $\frac{12.0}{7.11}$ and express the answer to the correct number of significant figures.
2. 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 result should have three significant figures.
3. Performing the division
The result of the division is $\frac{12.0}{7.11} = 1.6877637130801686$. We need to round this result to three significant figures.
4. Rounding to correct number of significant figures
Rounding 1.6877637130801686 to three significant figures gives us 1.69.
5. Final Answer
Therefore, the solution to the problem expressed to the correct number of significant figures is 1.69.
### Examples
In a science experiment, you might need to divide the mass of a substance by its volume to find its density. If your measurements are 12.0 grams and 7.11 cubic centimeters, you would calculate the density as 12.0/7.11. Expressing the result with the correct number of significant figures (1.69 g/cm³) ensures your calculation reflects the precision of your measurements, preventing misleading conclusions about the substance's properties.
