Significant Figures Summary

Rules for Significant Figures

Importance of Significant Figures

  • Measurement precision is limited by the measuring tool used.
  • Significant figures convey the accuracy of measurements and calculations.

Rule 1: Identifying Significant Figures

  • Count from the first nonzero digit (left to right).
  • All nonzero digits are significant.
  • Zeros between nonzero digits are significant.
  • Trailing zeros are significant only with a decimal point.
    • Example: 502.00 has five sig figs, while 100,000 has one.
  • Leading zeros before the first nonzero digit are not significant.
    • Example: 0.0007 has one sig fig.

Rule 2: Adding and Subtracting with Significant Figures

  • Result cannot be more precise than the least precise number.
  • Round to the same place value as the least precise number.
    • Example: 3.019 + 3.2 + 7.66 - 13.9 is rounded to tenths place.

Rule 3: Multiplying and Dividing with Significant Figures

  • Result cannot be more precise than the least precise number.
  • Result must have the same number of significant figures as the number with the fewest sig figs.
    • Example: 421 × 52.42 = 22,100 (three sig figs), while 1,500 + 345 = 4.3 (two sig figs).