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Significant Figures Overview

Oct 8, 2025

Overview

This lecture explains the concept of significant figures, how to identify them in various numbers, and why they matter in representing measurement precision.

Purpose of Significant Figures

  • Significant figures reflect the precision of measured values.
  • Do not report more digits than the measurement's actual precision allows.

Identifying Significant Figures in Examples

  • Leading zeros (zeros before the first non-zero digit) are not significant.
  • All non-zero digits are always significant.
  • Trailing zeros after a decimal point are significant, as they indicate measured precision.
  • Zeros between non-zero digits are significant.
  • For a number like 0.00700, only the "7", "0", and "0" after the decimal are significant (3 significant figures).
  • 0.052 has two significant figures (5 and 2).
    1. (with a written decimal) has three significant figures; the decimal indicates precision includes the zero.
  • 52,000 without a decimal is ambiguous—assume only non-zero digits are significant unless a decimal shows extra precision.

Rules of Thumb for Significant Figures

  • Ignore leading zeros.
  • Count all non-zero digits and any zeros between or after significant digits if a decimal is present.
  • A decimal point at the end signals that all digits shown are significant.
  • Absence of a decimal in numbers ending with zeros leads to ambiguity in significant figures.

Key Terms & Definitions

  • Significant figures — digits in a number that reflect the precision of a measured value.
  • Leading zeros — zeros before the first non-zero digit; not significant.
  • Trailing zeros — zeros after the last non-zero digit; significant only if a decimal point is present.
  • Precision — the degree to which a measurement is refined.

Action Items / Next Steps

  • Practice identifying significant figures in various numbers.
  • Formalize rules for significant figures using additional examples.