Chemistry Significant Figures Worksheet Answers

Mastering Significant Figures: A Comprehensive Guide with Worked Examples and Practice Problems

Understanding significant figures is crucial in chemistry and other scientific fields. It's all about accurately representing the precision of measurements and calculations. This comprehensive guide will walk you through the rules, provide detailed examples, and offer a worksheet with answers to solidify your understanding. By the end, you’ll confidently handle significant figures in your scientific work. This article covers everything from basic rules to more complex calculations involving multiplication, division, addition, and subtraction.

Introduction to Significant Figures

Significant figures (also known as significant digits) reflect the certainty of a measurement. They indicate the precision of your measuring instrument and the level of accuracy you can report. The more significant figures, the more precise the measurement. For instance, a mass recorded as 10.00g is more precise than a mass recorded as 10g. The former indicates precision to the hundredth of a gram, while the latter only shows precision to the nearest gram. Mastering significant figures is essential for accurate data reporting and analysis in chemistry and beyond. Improper handling can lead to significant errors in calculations and conclusions.

Rules for Determining Significant Figures

Before diving into calculations, let's establish the fundamental rules for determining the number of significant figures in a given number:

1. Non-zero digits are always significant. The number 25.3 has three significant figures.

2. Zeros between non-zero digits are always significant. The number 1005 has four significant figures.

3. Leading zeros (zeros to the left of the first non-zero digit) are never significant. They only serve to locate the decimal point. The number 0.0025 has two significant figures (2 and 5).

4. Trailing zeros (zeros to the right of the last non-zero digit) 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. In scientific notation (a x 10^b), all digits in 'a' are significant. The number 2.50 x 10³ has three significant figures.

Significant Figures in Calculations: Addition and Subtraction

When adding or subtracting numbers, the result should have the same number of decimal places as the measurement with the fewest decimal places.

Example 1:

12.34 + 5.6 + 101.234 = ?

• 12.34 has two decimal places
• 5.6 has one decimal place
• 101.234 has three decimal places

The measurement with the fewest decimal places is 5.6 (one decimal place). Therefore, the final answer should be rounded to one decimal place:

12.34 + 5.6 + 101.234 = 119.174 ≈ 119.2

Example 2:

100.0 - 98.765 = ?

• 100.0 has one decimal place
• 98.765 has three decimal places

The answer should be rounded to one decimal place:

100.0 - 98.765 = 1.235 ≈ 1.2

Significant Figures in Calculations: Multiplication and Division

When multiplying or dividing numbers, the result should have the same number of significant figures as the measurement with the fewest significant figures.

Example 3:

2.5 x 3.456 = ?

• 2.5 has two significant figures
• 3.456 has four significant figures

The answer should have two significant figures:

2.5 x 3.456 = 8.64 ≈ 8.6

Example 4:

123.456 / 2.3 = ?

• 123.456 has six significant figures
• 2.3 has two significant figures

The answer should have two significant figures:

123.456 / 2.3 = 53.6765 ≈ 54

Exact Numbers and Significant Figures

Exact numbers, such as counting numbers (e.g., 12 apples) or defined constants (e.g., exactly 12 inches in a foot), have an infinite number of significant figures and do not limit the significant figures in a calculation.

Rounding Rules

When rounding numbers, follow these rules:

• If the digit to be dropped is less than 5, round down. For example, 12.34 rounded to one decimal place is 12.3.
• If the digit to be dropped is greater than 5, round up. For example, 12.36 rounded to one decimal place is 12.4.
• If the digit to be dropped is exactly 5, round to the nearest even number. For example, 12.35 rounds to 12.4, and 12.45 rounds to 12.4. This method helps avoid systematic bias in rounding.

Scientific Notation and Significant Figures

Scientific notation is a useful way to express very large or very small numbers. It also clearly shows the number of significant figures. For example, 2.50 x 10⁴ clearly shows three significant figures.

Significant Figures Worksheet with Answers

Here's a worksheet with practice problems to test your understanding. Remember to apply the rules discussed above.

Part 1: Determining Significant Figures

1. How many significant figures are in 2500?
2. How many significant figures are in 0.00250?
3. How many significant figures are in 10.005?
4. How many significant figures are in 1.02 x 10^-3?
5. How many significant figures are in 120,000.0?

Part 2: Addition and Subtraction

1. 12.34 + 5.678 - 2.1 = ?
2. 100.0 - 99.99 = ?
3. 0.0023 + 1.2345 + 0.1 = ?

Part 3: Multiplication and Division

1. 2.5 x 3.4567 = ?
2. 1234.56 / 2.5 = ?
3. 0.005 x 10.00 = ?

Part 4: Mixed Calculations

1. (12.34 + 5.6) / 2.5 = ?
2. (100.0 – 98.7) x 2.345 = ?

Answers:

Part 1:

1. 2
2. 3
3. 5
4. 3
5. 7

Part 2:

1. 15.9
2. 0.01
3. 1.337

Part 3:

1. 8.7
2. 494
3. 0.05

Part 4:

1. 7.2
2. 3.0

Conclusion

Understanding and applying the rules of significant figures is a fundamental skill for any scientist or student of science. It ensures the accuracy and precision of your calculations and results. By practicing regularly and carefully reviewing the rules, you'll develop confidence and proficiency in handling significant figures, contributing to more reliable and meaningful scientific work. Remember that while these rules are designed to maintain accuracy, understanding the underlying principles of measurement uncertainty is equally important for truly grasping the meaning of significant figures.