Significant Figures

Importance

• Significant figures are crucial in scientific measurements and calculations.
• They are essential for accurately reporting and interpreting data.
• Applied in calculations early in the course, and in second-semester lab work.

Definition

• Significant figures represent the number of meaningful digits in a measurement.
• Measurements contain uncertainty; significant figures help convey this uncertainty.
• Example: Reading volume in a graduated cylinder involves estimating the final digit.

Rules for Determining Significant Figures

1. Non-Zero Digits:

   • Always significant.
   • Example: 28.03 (all digits are significant).

2. Interior Zeros:

   • Zeros between non-zero digits are significant.
   • Example: 408 (the zero is significant), 7.0301 (both zeros are significant).

3. Leading Zeros:

   • Not significant.
   • Example: 0.0032 and 0.0006 (leading zeros are placeholders).

4. Trailing Zeros:

   • After a Decimal Place:
     • Significant.
     • Example: 45.000 (all zeros are significant), 3.560 (zero is significant).
   • Before a Decimal Place:
     • If a decimal is implied, zeros are ambiguous unless explicitly written.
     • Example: 1200 (ambiguous) vs. 1.200 × 10³ (all digits significant).

Scientific Notation

• Clarifies the number of significant figures.
• In 1.2 × 10³, two significant figures.
• In 1.20 × 10³, three significant figures.
• In 1.200 × 10³, four significant figures.

Exact Numbers

• Numbers with no uncertainty.
• Do not affect significant figures in calculations.
• Examples:
  • Counting discrete objects (e.g., three apples).
  • Defined conversions and constants (e.g., 100 cm in 1 m).
  • Numbers in equations (e.g., multiplying radius by two for diameter).