Significant Figures: Key Concepts and Examples

Determining Significant Figures

• Non-Zero Numbers: Always significant.
  • Example: 846 has 3 significant figures.
• Zeros Between Non-Zero Numbers: Always significant.
  • Example: 704 has 3 significant figures.
  • Example: 5006 has 4 significant figures.
• Trailing Zeros: Depends on the presence of a decimal point.
  • Without Decimal: Not significant (e.g., 500 has 1 significant figure).
  • With Decimal: Significant (e.g., 500.0 has 4 significant figures).
• Leading Zeros: Never significant.
  • Example: 0.075 has 2 significant figures.
  • Example: 0.00836 has 3 significant figures.

Examples and Exercises

• Example: 0.0050830

  • Leading zeros are not significant.
  • Zeros between non-zero numbers and trailing zeros (with decimal) are significant.
  • Total significant figures: 5.

• Quiz Examples:

  • 42.50: 3 significant figures (trailing zero not counted without decimal).
  • 7080: 3 significant figures (trailing zero not counted without decimal).
  • 1050.: 5 significant figures (trailing zero counted with decimal).
  • 0.00703: 3 significant figures (leading zeros not counted).
  • 0.08060: 4 significant figures (leading zeros not counted, trailing zero after decimal counted).
  • 5030.0: 5 significant figures (trailing zero counted with decimal).
  • 750.064080: 9 significant figures (all zeros between non-zeros counted, trailing zero after decimal counted).

Rounding Based on Significant Figures

• Multiplication/Division: Round to the least number of significant figures in the original numbers.

  • Example: 4.6 (2 sig figs) x 3.52 (3 sig figs) = 16.192 → round to 16 (2 sig figs).
  • Example: 5.64 (3 sig figs) x 12.458 (5 sig figs) = 70.26312 → round to 70.3 (3 sig figs).

• Addition/Subtraction: Round to the least number of decimal places in the original numbers.

  • Example: 2.36 + 12.1 = 14.46 → round to 14.5 (round based on least decimal places).
  • Example: 4.328 + 13 + 5.45 = 22.8 → round to 23 (round based on the least decimal places).

Additional Resources

• For more in-depth examples and exercises on significant figures, refer to the longer video link provided in the video description.
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