Chemistry Significant Digits Worksheet Answers

Mastering Significant Digits: A Comprehensive Guide with Worksheet Answers

Understanding significant digits (also known as significant figures or sig figs) is crucial in chemistry and other scientific fields. Accurate calculations depend on correctly identifying and using significant figures to reflect the precision of measurements. This article provides a comprehensive guide to significant digits, including rules for determining them, performing calculations with them, and ultimately, providing answers to a practice worksheet. This will equip you with the necessary skills to confidently handle significant figures in your scientific endeavors.

Understanding Significant Digits

Significant digits represent the reliable digits in a measurement. They reflect the precision of the measuring instrument and the skill of the person making the measurement. The more significant digits, the more precise the measurement. For example, a measurement of 12.34 cm is more precise than a measurement of 12 cm because it has more significant digits. Understanding significant figures is crucial for correctly reporting and interpreting experimental data.

Rules for Determining Significant Digits

Here are the fundamental rules to determine the number of significant figures in a number:

1. Non-zero digits are always significant. For example, in the number 234, all three digits are significant.

2. Zeros between non-zero digits are always significant. In the number 204, the zero is significant.

3. Leading zeros (zeros to the left of the first non-zero digit) are never significant. They only serve to place the decimal point. For example, in 0.0025, only 2 and 5 are significant.

4. Trailing zeros (zeros to the right of the last non-zero digit) are significant only if the number contains a decimal point. In 250, only 2 and 5 are significant. However, in 250.0, all four digits are significant. Similarly, 250. or 2.50 x 10² have three significant figures.

5. Exact numbers have an infinite number of significant digits. These are often counting numbers (e.g., 12 apples) or defined constants (e.g., exactly 12 inches in a foot). They don't limit the number of significant figures in a calculation.

Significant Digits in Calculations

When performing calculations with measured values, the number of significant figures in the result must reflect the precision of the input values. Different rules apply for addition/subtraction and multiplication/division.

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 Off

Rounding is necessary to ensure the final answer has the correct number of significant figures. The general rule is:

• If the digit to be dropped is less than 5, round down (drop the digit).
• If the digit to be dropped is 5 or greater, round up (increase the preceding digit by 1).

Scientific Notation and Significant Figures

Scientific notation is a useful way to represent very large or very small numbers while clearly indicating the number of significant figures. The number is written in the form a x 10^b, where 'a' is a number between 1 and 10, and 'b' is an integer exponent. Only the digits in 'a' are significant. For example, 2.50 x 10³ has three significant figures.

Practice Worksheet and Answers

Let's test your understanding with a worksheet. Remember to apply the rules of significant figures carefully in each calculation.

Worksheet:

1. Determine the number of significant figures in each of the following numbers: a) 3.14159 b) 0.0025 c) 2500 d) 2500. e) 2.50 x 10³ f) 1000

2. Perform the following calculations and report the answer with the correct number of significant figures: a) 25.43 + 1.2 + 0.057 b) 125.0 – 2.345 c) 25.2 x 3.14 d) 125 / 2.50 e) (1.23 x 10²) + (4.5 x 10¹) f) (2.5 x 10³) / (5.0 x 10^-2)

3. A rectangular block is measured to be 12.5 cm long, 5.0 cm wide, and 2.0 cm high. Calculate the volume of the block, and express your answer with the correct number of significant figures.

4. A student measured the mass of an object three times: 25.2 g, 25.1 g, and 25.3 g. Calculate the average mass and express it with the correct number of significant figures.

Answers:

1. a) 6 b) 2 c) 2 d) 4 e) 3 f) 1 (Unless it's specifically stated otherwise, trailing zeros without a decimal point are not significant)

2. a) 26.7 (The fewest decimal places is one) b) 122.7 (The fewest decimal places is one) c) 79.2 (The fewest significant figures is three) d) 50.0 (The fewest significant figures is three) e) 1.68 x 10² (Remember to align decimals before adding) f) 5.0 x 10⁴ (The fewest significant figures is two)

3. Volume = length x width x height = 12.5 cm x 5.0 cm x 2.0 cm = 125 cm³ (The fewest significant figures is two)

4. Average mass = (25.2 g + 25.1 g + 25.3 g) / 3 = 25.2 g (Note that the average should be reported with the same precision as the individual measurements.)

Frequently Asked Questions (FAQ)

Q: What happens if I have a calculation with different numbers of significant figures?

A: You must follow the rules for addition/subtraction and multiplication/division separately, then round your final answer to the correct number of significant figures according to the least precise measurement involved in the calculation.

Q: Are all zeros significant?

A: No. Leading zeros (zeros before the first non-zero digit) are not significant. Trailing zeros are significant only if the number contains a decimal point. Zeros between non-zero digits are always significant.

Q: How do I handle calculations involving both addition/subtraction and multiplication/division?

A: Handle addition/subtraction first, then multiplication/division. Round to the correct number of significant figures after each operation, following the appropriate rules for each.

Conclusion

Mastering significant digits is a fundamental skill in chemistry. By understanding the rules for determining, calculating with, and rounding significant figures, you can ensure the accuracy and reliability of your scientific calculations. This comprehensive guide, along with the practice worksheet and answers, should provide you with a solid foundation. Remember to always pay attention to detail and practice regularly to build proficiency. Accurate reporting and interpretation of scientific data rely heavily on a firm grasp of significant figures. The more you practice, the more confident you will become!