Rules of Significant Figures

Main ideas / lesson conveyed

• Significant figures are the digits in a measurement that are meaningful (reflecting certainty and estimation).
• In any measured value, all certain digits count, and the last digit (estimated by the instrument/observer) also counts—so the estimated digit is always the last significant figure.
• Whether a digit is significant depends primarily on:
  • zero placement
  • whether a decimal point is present (for trailing zeros)
  • whether zeros are leading, confined (captive), or trailing

Rules for determining significant figures (detailed)

Rule 1: Non-zero digits

• Any digit 1–9 is automatically significant.
• Examples:
  • 1562 → 4 significant figures
  • 43.6 → 3 significant figures (3, 4, and estimated 6)
  • 147 → includes the estimated last digit as significant (e.g., in examples like 0.7 pounds)

Rule 2: Leading zeros

• Zeros at the beginning of a number (leading zeros) are never significant.
• Examples:
  • 0.3 → 1 significant figure
  • 0.0005 → 1 significant figure (only the 5)

Rule 3: Confined / captive zeros

• Zeros between two non-zero digits are always significant.
• Examples:
  • 305 → 3 significant figures
  • 120009 (e.g., 1 2 0 0 0 9) → all zeros between 2 and 9 count
  • 3.005 → zeros between 3 and 5 count as significant
  • 120.09 → both zeros count if sandwiched between non-zero digits

Rule 4: Trailing zeros

• Trailing zeros are zeros at the end of a number.
• Key dependency: whether the decimal point is present

If the decimal point is present

• Trailing zeros are significant.
• Examples:
  • 42.10 and 42.1 represent the same value, but the written zero in 42.10 indicates the measurement’s estimated digit, so 42.10 counts it.
  • 320.0 → 4 significant figures
  • 5.000 → trailing zeros are significant because the decimal point shows measurement precision

If the decimal point is absent

• Trailing zeros are not significant (placeholders).
• Examples:
  • 1200 → only 1 and 2 are significant
  • 1,200 (e.g., “one thousand two hundred”) → only the non-zero digits count
  • 30 → only 3 counts (unless a decimal point is shown)

Note: You only need to treat the decimal point as critical when dealing with trailing zeros.

Special case: conversion factors / exact numbers

• Conversion factors (e.g., 1 foot = 12 inches, 1 hour = 60 minutes, 1 meter = 10 decimeters) are treated as exact numbers.
• Therefore:
  • They have infinite/unlimited significant figures.
  • If a conversion factor is involved, the significant figures count is ∞ (infinite).

Additional handling: scientific notation

• In scientific notation, ignore the exponent part (the power-of-ten component).
• Count significant figures only from the coefficient part.
• Trailing zeros in the coefficient (when a decimal point is present) count as significant.

Practice/example breakdowns included

Worked example: 0.00204

• Leading zeros: 0.00 → not significant
• 2 and 4: non-zero digits → significant
• 0 between 2 and 4: confined zero → significant
• Trailing zero counting depends on whether it is a trailing zero with a decimal point.
• Final result given: 4 significant figures

Lettered test set (a–g)

• a: 2 significant figures (leading zeros ignored)
• b: 4 significant figures (confined zero + trailing zero with decimal point both count)
• c: 4 significant figures (all non-zero digits)
• d: 3 significant figures (scientific notation: ignore exponent part)
• e: infinite significant figures (conversion factor / exact number)
• f: 5 significant figures (trailing zeros with decimal point count)
• g: 1 significant figure (trailing zeros without decimal point are placeholders)

Speakers / sources

• Speaker: The instructor/teacher (only “hello everybody…” is shown; no name provided)
• Video title/source: “Rules of Significant Figures” (YouTube video)