Significant Figures and Scientific Notation

Introduction to Measurement in Chemistry

Accurate measurement is fundamental in chemistry, as it allows scientists to quantify substances and reactions. Understanding how to properly record and interpret measurements is essential for reliable experimental results.

• Measurement: The process of obtaining the magnitude of a quantity relative to a standard unit.

• Uncertainty: All measurements have some degree of uncertainty due to limitations in instruments and human observation.

Significant Figures

Significant figures (sig figs) are the digits in a measurement that are known with certainty plus one digit that is estimated. They reflect the precision of a measured or calculated quantity.

• Definition: All the nonzero digits and any zeros between them or after the decimal point in a measurement.

• Rules for Counting Significant Figures:

  • All nonzero digits are significant.

  • Zeros between nonzero digits are significant.

  • Leading zeros (zeros before the first nonzero digit) are not significant.

  • Trailing zeros in a number containing a decimal point are significant.

  • Trailing zeros in a whole number with no decimal shown are ambiguous.

• Example: 0.00450 has three significant figures (4, 5, and the trailing 0).

Scientific Notation

Scientific notation is a method of expressing very large or very small numbers in the form a × 10n, where a is a number between 1 and 10, and n is an integer. This notation simplifies calculations and clearly indicates the number of significant figures.

• Format:

• Example: 0.00032 =

• Moving the Decimal: Move the decimal to create a number between 1 and 10; count the places moved to determine the exponent.

Mathematical Operations with Significant Figures

When performing calculations, the number of significant figures in the result should reflect the precision of the measurements used.

• 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 (Multiplication): (rounded to two significant figures)

• Example (Addition): (rounded to one decimal place)

Exact Numbers

Exact numbers have an infinite number of significant figures and do not limit the number of significant figures in a calculation. These include counted values and defined quantities (e.g., 1 dozen = 12).

• Example: 100 cm = 1 m (exact by definition)

Summary Table: Rules for Significant Figures

Additional info:

Understanding significant figures and scientific notation is foundational for all subsequent topics in general chemistry, as it ensures clarity and accuracy in reporting and interpreting experimental data.