Part of JME-07 — Units, Measurements & Error Analysis

Significant Figures Rules

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Counting SF:

  1. Non-zero digits: always significant (345 = 3 SF)
  2. Zeros between non-zero: significant (3005 = 4 SF)
  3. Leading zeros: NOT significant (0.0034 = 2 SF)
  4. Trailing zeros after decimal: significant (3.400 = 4 SF)
  5. Trailing zeros without decimal: ambiguous (2300 = 2, 3, or 4 SF — use scientific notation)

Arithmetic rules:

  • Multiplication/Division: result has fewest SF of inputs
  • Addition/Subtraction: result has fewest decimal places of inputs
  • Exact numbers (2 in circumference = 2pir, defined values): infinite SF

Examples:

  • 3.24 * 2.1 = 6.804 -> 6.8 (2 SF)
  • 3.24 + 2.1 = 5.34 -> 5.3 (1 decimal place)
  • 0.020300 has 5 SF (only leading zeros don't count)

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