Significant Figures: A Quick Review

Determining Significant Figures

• Non-Zero Numbers: Every non-zero number is a significant figure.

  • Example: 846 has 3 significant figures.
  • Example: 3546 has 4 significant figures.

• Zeros Between Non-Zero Numbers: Zeros between non-zero numbers are significant.

  • Example: 704 has 3 significant figures.
  • Example: 5006 has 4 significant figures.

• Trailing Zeros: Zeros to the right of a non-zero number.

  • Without Decimal Point: Not significant.
    • Example: 500 has 1 significant figure.
  • With Decimal Point: Significant.
    • Example: 500. has 3 significant figures.
    • Example: 500.0 has 4 significant figures.

• Leading Zeros: Zeros to the left of the first non-zero number are not significant.

  • Example: 0.075 has 2 significant figures (7 and 5).
  • Example: 0.00836 has 3 significant figures.

Practice Example

• Number: 0.0050830
  • Analysis:
    • Leading zeros are not significant.
    • Zeros between non-zero numbers are significant.
    • Trailing zeros are significant if there is a decimal point.
  • Significant Figures: 5

Quiz Example

• 42.50 - 4 significant figures
• 7080 - 4 significant figures (without decimal point, zero is not counted)
• 1000.50 - 6 significant figures
• 0.00703 - 3 significant figures
• 0.08060 - 4 significant figures
• 5030.0 - 5 significant figures
• 750.064080 - 9 significant figures

Rounding with Significant Figures

• Multiplication/Division Rule: Round your answer 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 → Rounded to 16 (2 sig figs)

• Practice:

  • 5.64 x 12.458 = 70.26312 → Rounded to 70.3 (3 sig figs)
  • 96.752 ÷ 3.541 = 27.32335498 → Rounded to 27.32 (4 sig figs)

Addition/Subtraction Rule

• Round answer to the least number of digits to the right of the decimal point.
  • Example: 2.36 + 12.1 = 14.46 → Rounded to 14.5
  • Example: 4.328 + 13 + 5.45 = 22.778 → Rounded to 23

Additional Resources

• For more problems and detailed explanations, refer to the longer video available in the description section of the video.
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