What Is The Final Correct Answer To The Proper Number Of Significant Digits?A. 17.2 GB. 17.24 GC. 69.0 GD. 68.95 G
Understanding Significant Figures
Significant figures are a way to express the precision of a measurement. They are used to indicate the number of digits that are known to be reliable and certain in a measurement. In other words, they represent the degree of accuracy of a measurement. The number of significant figures in a measurement depends on the instrument used to make the measurement, the technique used, and the level of precision required.
Rules for Determining Significant Figures
There are several rules for determining the number of significant figures in a measurement. These rules are as follows:
- Non-zero digits are always significant: Any non-zero digit in a measurement is considered significant.
- Zeros between non-zero digits are significant: Zeros that appear between non-zero digits are considered significant.
- Leading zeros are not significant: Zeros that appear at the beginning of a measurement are not considered significant.
- Trailing zeros in a measurement with a decimal point are significant: Zeros that appear after a decimal point in a measurement are considered significant.
- Trailing zeros in a measurement without a decimal point are not significant: Zeros that appear at the end of a measurement without a decimal point are not considered significant.
- Zeros in a measurement with a decimal point and a power of 10 are significant: Zeros that appear in a measurement with a decimal point and a power of 10 are considered significant.
Determining the Number of Significant Figures in a Measurement
To determine the number of significant figures in a measurement, we need to apply the rules mentioned above. Let's consider the following measurements:
- 17.2 g: In this measurement, the non-zero digits 1, 7, and 2 are significant. The zero between the 1 and 7 is also significant. Therefore, the number of significant figures in this measurement is 4.
- 17.24 g: In this measurement, the non-zero digits 1, 7, 2, and 4 are significant. The zeros between the 1 and 7 and between the 2 and 4 are also significant. Therefore, the number of significant figures in this measurement is 5.
- 69.0 g: In this measurement, the non-zero digits 6 and 9 are significant. The zero between the 6 and 9 is also significant. Therefore, the number of significant figures in this measurement is 3.
- 68.95 g: In this measurement, the non-zero digits 6, 8, 9, and 5 are significant. The zeros between the 6 and 8 and between the 9 and 5 are also significant. Therefore, the number of significant figures in this measurement is 5.
Conclusion
In conclusion, the number of significant figures in a measurement depends on the instrument used to make the measurement, the technique used, and the level of precision required. By applying the rules mentioned above, we can determine the number of significant figures in a measurement. The correct answer to the question "What is the final correct answer to the proper number of significant digits?" is B. 17.24 g, which has 5 significant figures.
Key Takeaways
- Significant figures are a way to express the precision of a measurement.
- The number of significant figures in a measurement depends on the instrument used to make the measurement, the technique used, and the level of precision required.
- There are several rules for determining the number of significant figures in a measurement.
- By applying the rules mentioned above, we can determine the number of significant figures in a measurement.
Common Mistakes to Avoid
- Not considering leading zeros: Leading zeros are not significant and should not be counted when determining the number of significant figures in a measurement.
- Not considering trailing zeros in a measurement without a decimal point: Trailing zeros in a measurement without a decimal point are not significant and should not be counted when determining the number of significant figures in a measurement.
- Not considering zeros in a measurement with a decimal point and a power of 10: Zeros in a measurement with a decimal point and a power of 10 are significant and should be counted when determining the number of significant figures in a measurement.
Real-World Applications
- Scientific research: Significant figures are used in scientific research to express the precision of measurements and to determine the accuracy of results.
- Engineering: Significant figures are used in engineering to express the precision of measurements and to determine the accuracy of results.
- Quality control: Significant figures are used in quality control to express the precision of measurements and to determine the accuracy of results.
Final Thoughts
Frequently Asked Questions
Q: What are significant figures?
A: Significant figures are a way to express the precision of a measurement. They are used to indicate the number of digits that are known to be reliable and certain in a measurement.
Q: Why are significant figures important?
A: Significant figures are important because they help to express the precision of a measurement and to determine the accuracy of results. They are used in scientific research, engineering, and quality control to ensure that measurements are accurate and reliable.
Q: How do I determine the number of significant figures in a measurement?
A: To determine the number of significant figures in a measurement, you need to apply the rules mentioned below:
- Non-zero digits are always significant.
- Zeros between non-zero digits are significant.
- Leading zeros are not significant.
- Trailing zeros in a measurement with a decimal point are significant.
- Trailing zeros in a measurement without a decimal point are not significant.
- Zeros in a measurement with a decimal point and a power of 10 are significant.
Q: What is the difference between significant figures and decimal places?
A: Significant figures and decimal places are related but distinct concepts. Significant figures express the precision of a measurement, while decimal places express the number of digits in a measurement.
Q: How do I round a measurement to the correct number of significant figures?
A: To round a measurement to the correct number of significant figures, you need to apply the following rules:
- If the digit to be rounded is less than 5, you round down.
- If the digit to be rounded is 5 or greater, you round up.
Q: What is the correct answer to the question "What is the final correct answer to the proper number of significant digits?"
A: The correct answer to the question "What is the final correct answer to the proper number of significant digits?" is B. 17.24 g, which has 5 significant figures.
Q: Can you provide examples of how to determine the number of significant figures in a measurement?
A: Here are some examples:
- 17.2 g: In this measurement, the non-zero digits 1, 7, and 2 are significant. The zero between the 1 and 7 is also significant. Therefore, the number of significant figures in this measurement is 4.
- 17.24 g: In this measurement, the non-zero digits 1, 7, 2, and 4 are significant. The zeros between the 1 and 7 and between the 2 and 4 are also significant. Therefore, the number of significant figures in this measurement is 5.
- 69.0 g: In this measurement, the non-zero digits 6 and 9 are significant. The zero between the 6 and 9 is also significant. Therefore, the number of significant figures in this measurement is 3.
- 68.95 g: In this measurement, the non-zero digits 6, 8, 9, and 5 are significant. The zeros between the 6 and 8 and between the 9 and 5 are also significant. Therefore, the number of significant figures in this measurement is 5.
Q: Can you provide examples of how to round a measurement to the correct number of significant figures?
A: Here are some examples:
- 17.24 g: If we want to round this measurement to 3 significant figures, we would round it to 17.2 g.
- 69.0 g: If we want to round this measurement to 2 significant figures, we would round it to 70 g.
- 68.95 g: If we want to round this measurement to 3 significant figures, we would round it to 69.0 g.
Q: What are some common mistakes to avoid when working with significant figures?
A: Some common mistakes to avoid when working with significant figures include:
- Not considering leading zeros.
- Not considering trailing zeros in a measurement without a decimal point.
- Not considering zeros in a measurement with a decimal point and a power of 10.
- Rounding a measurement incorrectly.
Q: What are some real-world applications of significant figures?
A: Significant figures have many real-world applications, including:
- Scientific research: Significant figures are used in scientific research to express the precision of measurements and to determine the accuracy of results.
- Engineering: Significant figures are used in engineering to express the precision of measurements and to determine the accuracy of results.
- Quality control: Significant figures are used in quality control to express the precision of measurements and to determine the accuracy of results.
Q: Can you provide any final thoughts on significant figures?
A: In conclusion, significant figures are an important concept in chemistry and other scientific fields. By understanding the rules for determining significant figures, we can express the precision of measurements and determine the accuracy of results. The correct answer to the question "What is the final correct answer to the proper number of significant digits?" is B. 17.24 g, which has 5 significant figures.