Significant Figures Worksheet Answers: Clear & Concise Guide
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Significant figures are an essential part of scientific measurement, helping to convey the precision of calculated values. They represent the digits in a number that contribute to its accuracy, ensuring that the results of calculations are reliable. This article provides a comprehensive guide to understanding significant figures, with explanations, rules, examples, and a sample worksheet with answers.
Understanding Significant Figures
What Are Significant Figures?
Significant figures, also known as significant digits, are the digits in a number that are reliable and convey meaningful information. These digits include all the non-zero numbers, any zeros between significant digits, and trailing zeros when there is a decimal point present.
Rules for Determining Significant Figures
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Non-Zero Digits: All non-zero digits are significant.
- Example: 123 has three significant figures.
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Leading Zeros: Leading zeros (zeros before non-zero digits) are not significant.
- Example: 0.0045 has two significant figures (4 and 5).
-
Captive Zeros: Zeros between non-zero digits are significant.
- Example: 105 has three significant figures.
-
Trailing Zeros:
- Trailing zeros in a whole number without a decimal point are not significant.
- Example: 1500 has two significant figures.
- Trailing zeros in a decimal number are significant.
- Example: 1500. has four significant figures.
- Trailing zeros in a whole number without a decimal point are not significant.
-
Exact Numbers: Numbers that are counted or defined quantities have an infinite number of significant figures.
- Example: 100 students (exact number) has infinite significant figures.
Performing Calculations with Significant Figures
When performing calculations, significant figures are crucial in ensuring that the precision of your results is maintained. Here are the basic rules:
Addition and Subtraction
In addition and subtraction, the result should have the same number of decimal places as the value with the least number of decimal places.
| Example | Calculation | Significant Figures in Result |
|---|---|---|
| 12.11 | + 0.3 | 12.41 (1 decimal place) |
| 12.1 | + 0.32 | 12.4 (1 decimal place) |
Multiplication and Division
In multiplication and division, the result should have the same number of significant figures as the value with the least significant figures.
| Example | Calculation | Significant Figures in Result |
|---|---|---|
| 4.56 | × 1.4 | 6.4 (2 significant figures) |
| 0.0023 | × 250 | 0.58 (2 significant figures) |
Sample Worksheet
Here is a simple worksheet to practice identifying significant figures and performing calculations. Below are some questions followed by their answers.
Questions
- How many significant figures are in the number 0.00560?
- Round the number 76.845 to three significant figures.
- Calculate: 25.3 + 0.004 + 1.2
- Calculate: 6.7 × 2.5
Answers
- Significant Figures: 3 (5, 6, and the trailing 0).
- Rounded Number: 76.8
- Sum: 26.5 (1 decimal place).
- Product: 17 (2 significant figures).
Important Notes
When working with significant figures, it's crucial to retain the integrity of measurements and calculations. This not only reflects the precision of your work but also ensures accurate communication in scientific contexts.
Conclusion
Understanding significant figures is vital for anyone involved in scientific work. They help maintain clarity and precision in measurements, ensuring that results are reliable and meaningful. Through this guide and practice worksheet, you can hone your skills in determining and utilizing significant figures effectively. Remember to follow the rules diligently, as they are essential for accurate scientific communication. Happy calculating!