OrgTube Video Lecture: Significant Figures

Introduction

• Topic: Significant Figures
  • Used to show the level of certainty in measurements.
  • More significant figures indicate more certainty.

Determining Significant Figures

Basic Rules

1. Non-zero Digits:

   • All non-zero digits are significant.
   • Examples:
     • Five non-zero digits = 5 significant figures.
     • Three non-zero digits = 3 significant figures.
     • Four non-zero digits = 4 significant figures.

2. Zeros Between Non-zero Digits:

   • Always significant.
   • Examples:
     • Five significant figures.
     • Three significant figures.
     • Four significant figures.

3. Leading Zeros:

   • Not significant.
   • Examples:
     • Three significant figures.
     • Three significant figures.
     • One significant figure.

4. Trailing Zeros:

   • Not significant unless after a decimal point.
   • Examples:
     • Without decimal point: 2 significant figures.
     • With decimal point: 3 significant figures.
     • Trailing zero with decimal point: 4 significant figures.

5. Scientific Notation:

   • Ignore 10’s exponent part.
   • Example: 5.10 has 3 significant figures.

Application in Calculations

Rounding Rules

• Rounding Off:
  • Examine the next digit after the last significant figure.
  • Less than 5: do not change the last digit.
  • More than 5: add 1 to the last digit.
• Special Case for 5:
  • If preceding digit is even, do not change.
  • If odd, increase by one.

Calculation Rules

• Addition and Subtraction:

  • Final answer should have the least decimal places from the numbers involved.
  • Example:
    • 2.04 + 4.476 = 6.516
    • Report as 6.52 based on two decimal places.

• Multiplication and Division:

  • Final answer should have the least number of significant figures from the numbers involved.
  • Example:
    • Multiplication: 9.556... with 3 significant figures.
    • Report as 9.56.

Complex Operations

• Keep all digits in calculations until the very end.
• Example Operations:
  • Addition first, then multiplication: Example of using parentheses.
  • Division first, then addition: Based on operator priority.

Conclusion

• Final answers should reflect the significant figures as per rules.
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