Measurement, Significant Figures, and Calculations in Chemistry

Matter and Measurements

Scientific Notation

Scientific notation is a method used to express very large or very small numbers in a compact form. It is commonly used in chemistry to handle measurements and calculations efficiently.

• Format: A number is written as a × 10n, where 1 ≤ a < 10 and n is an integer.

• Example: 0.00056 = 5.6 × 10-4

Error, Accuracy, and Precision

Understanding the reliability of measurements is crucial in chemistry.

• Accuracy: How close a measured value is to the true or accepted value.

• Precision: How close repeated measurements are to each other, regardless of accuracy.

• Error: The difference between a measured value and the true value.

• Types of Error: Systematic (consistent, repeatable) and random (unpredictable variations).

• Example: Measuring a 10.0 mL sample and obtaining 9.8 mL, 9.9 mL, and 10.1 mL shows good precision but slight inaccuracy.

Significant Figures

Significant figures (sig figs) indicate the precision of a measured or calculated quantity.

• Rules for Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros are not significant.

  • Trailing zeros are significant only if there is a decimal point.

• Example: 0.00450 has three significant figures.

Calculations with Measured Numbers

When performing calculations, the number of significant figures in the result depends on the operation:

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

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

• Example (Addition): 12.11 + 0.3 = 12.4 (one decimal place)

• Example (Multiplication): 4.56 × 1.4 = 6.4 (two significant figures)

Key Principle: Always round your final answer to the correct number of significant figures or decimal places based on the rules above.

Mathematical Operations and Functions

Basic mathematical operations (addition, subtraction, multiplication, division) are used frequently in chemistry calculations. Understanding how to handle significant figures in these operations is essential for accurate results.

• Practice: Use practice questions to reinforce your understanding of these rules.

Additional info:

• Conversion factors and dimensional analysis are important for unit conversions, but converting within the metric system itself is not covered in this section.