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Answer :
- Divide 12.0 by 7.11: $\frac{12.0}{7.11} = 1.6877637130801686$.
- Determine the number of significant figures: Both numbers have three significant figures.
- Round the result to three significant figures: $1.69$.
- 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 be rounded to 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 to three significant figures.
4. Rounding the Result
Rounding 1.6877637130801686 to three significant figures gives 1.69.
5. Final Answer
Therefore, the solution to the problem expressed to the correct number of significant figures is $\boxed{1.69}$.
### Examples
In chemistry, when calculating the concentration of a solution using molarity (moles per liter), you often divide the number of moles of solute by the volume of the solution. If you measure 12.0 grams of NaCl and dissolve it in 7.11 liters of water, you would perform a similar division. Expressing the result with the correct number of significant figures ensures the accuracy and reliability of your calculations and measurements in scientific experiments.
- Determine the number of significant figures: Both numbers have three significant figures.
- Round the result to three significant figures: $1.69$.
- 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 be rounded to 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 to three significant figures.
4. Rounding the Result
Rounding 1.6877637130801686 to three significant figures gives 1.69.
5. Final Answer
Therefore, the solution to the problem expressed to the correct number of significant figures is $\boxed{1.69}$.
### Examples
In chemistry, when calculating the concentration of a solution using molarity (moles per liter), you often divide the number of moles of solute by the volume of the solution. If you measure 12.0 grams of NaCl and dissolve it in 7.11 liters of water, you would perform a similar division. Expressing the result with the correct number of significant figures ensures the accuracy and reliability of your calculations and measurements in scientific experiments.
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