Significant Figures Worksheet Answers Chemistry

Mastering Significant Figures: A Comprehensive Guide with Worksheet Answers

Understanding significant figures is crucial for anyone working with scientific data, especially in chemistry. It's all about expressing the precision of your measurements and calculations accurately. This comprehensive guide will walk you through the rules of significant figures, provide worked examples, and offer solutions to a practice worksheet to solidify your understanding. Mastering significant figures ensures your calculations reflect the true accuracy of your experimental data and avoids misinterpretations based on imprecise reporting.

Introduction to Significant Figures

Significant figures (sig figs) represent the number of digits in a measurement that carry meaning contributing to its precision. They reflect the uncertainty inherent in any measurement. For example, if you measure the length of a table using a ruler marked in centimeters, you might measure 123 cm. This measurement has three significant figures. However, if you used a more precise measuring device, you might record 123.45 cm, giving you five significant figures. The more significant figures, the more precise the measurement. This article will detail the rules for determining significant figures and how to apply them in calculations.

Rules for Determining Significant Figures

Several rules guide us in identifying the number of significant figures in a given number:

1. All non-zero digits are significant. For example, in 245, there are three significant figures.

2. Zeros between non-zero digits are significant. In 1005, there are four significant figures.

3. Leading zeros (zeros to the left of the first non-zero digit) are not significant. In 0.0025, there are only two significant figures (2 and 5).

4. Trailing zeros (zeros at the end of a number) are significant only if the number contains a decimal point.

   • 100 has one significant figure.
   • 100. has three significant figures.
   • 100.0 has four significant figures.

5. Numbers in scientific notation are handled differently. In scientific notation (e.g., 1.23 x 10⁴), all digits in the coefficient (1.23) are significant. The exponent doesn't affect the number of significant figures.

Significant Figures in Calculations

When performing calculations with measurements, the number of significant figures in the result must reflect the precision of the input values.

Addition and Subtraction: The result should have the same number of decimal places as the measurement with the fewest decimal places.

Multiplication and Division: The result should have the same number of significant figures as the measurement with the fewest significant figures.

Rounding Rules

When rounding numbers to the correct number of significant figures, follow these rules:

1. If the digit to be dropped is less than 5, round down. For example, rounding 12.34 to two significant figures gives 12.

2. If the digit to be dropped is greater than or equal to 5, round up. Rounding 12.67 to two significant figures gives 13.

3. If the digit to be dropped is exactly 5, and it's followed by only zeros, round to the nearest even number. Rounding 12.50 to two significant figures gives 12. Rounding 13.50 to two significant figures gives 14.

Worked Examples

Let's illustrate these rules with some examples:

Example 1: Addition

Add the following measurements: 25.43 cm + 12.3 cm + 0.875 cm

• 25.43 cm has two decimal places.
• 12.3 cm has one decimal place.
• 0.875 cm has three decimal places.

The result, 38.605 cm, must be rounded to one decimal place (the fewest decimal places in the input measurements), resulting in 38.6 cm.

Example 2: Multiplication

Multiply the following measurements: 2.5 cm x 3.24 cm

• 2.5 cm has two significant figures.
• 3.24 cm has three significant figures.

The result, 8.1 cm², must be rounded to two significant figures (the fewest significant figures in the input measurements), resulting in 8.1 cm².

Example 3: Scientific Notation

Multiply 2.45 x 10³ cm by 3.1 x 10² cm.

The calculation yields 7.595 x 10⁵ cm². Rounding to two significant figures (limited by 3.1 x 10²), the answer is 7.6 x 10⁵ cm².

Significant Figures Worksheet with Answers

Here's a practice worksheet with answers to help you master significant figures:

Part 1: Identifying Significant Figures

Instructions: Determine the number of significant figures in each of the following numbers.

1. 125 (Answer: 3)
2. 0.0034 (Answer: 2)
3. 100.0 (Answer: 4)
4. 2001 (Answer: 4)
5. 0.02030 (Answer: 4)
6. 1.00 x 10^-3 (Answer: 3)
7. 5050 (Answer: 3)
8. 200 (Answer: 1)
9. 7.030 x 10⁴ (Answer: 4)
10. 0.000870 (Answer: 3)

Part 2: Calculations with Significant Figures

Instructions: Perform the following calculations and express your answers using the correct number of significant figures.

1. 12.34 + 5.6 + 0.002 (Answer: 18.0)
2. 25.3 - 10.87 (Answer: 14)
3. 12.5 x 3.45 (Answer: 43)
4. 100.0 / 2.5 (Answer: 40)
5. (1.23 x 10^-2) x (2.5 x 10⁴) (Answer: 3.1 x 10²)
6. (8.76 x 10⁵) / (2.4 x 10²) (Answer: 3.7 x 10³)
7. 23.45 + 1.234 + 0.0567 (Answer: 24.7)
8. 456.7 - 23.45 (Answer: 433.2)
9. 5.67 x 10³ / 2.3 **(Answer: 2.5 x 10³) **
10. 1.234 x 0.056 (Answer: 0.069)

Frequently Asked Questions (FAQ)

Q: Why are significant figures important in chemistry?

A: Significant figures are critical for accurately representing the precision of measurements and calculations. Using incorrect significant figures can lead to misleading conclusions about the accuracy of experimental data.

Q: What happens if I don't use the correct number of significant figures?

A: Failing to use correct significant figures introduces uncertainty and may lead to inaccurate results. It can also suggest a level of precision that doesn't exist in the original measurements.

Q: Are there situations where significant figures are not strictly followed?

A: In certain scenarios, like estimations or preliminary calculations, the strict application of significant figures may be relaxed. However, it's generally good practice to maintain accuracy whenever possible.

Q: How can I improve my understanding of significant figures?

A: Practice is key! Work through numerous problems, focusing on understanding the underlying rules and reasons. Consult reliable resources and seek assistance when needed.

Conclusion

Understanding and correctly applying significant figures is a fundamental skill in chemistry and other scientific disciplines. By following the rules outlined in this guide, you can ensure your calculations accurately reflect the precision of your measurements, leading to more reliable and trustworthy results. Remember to always consider the rules for addition/subtraction and multiplication/division, and practice consistently to build confidence and mastery. Through understanding and practice, significant figures will cease to be a challenge and become an integral part of your scientific calculations.