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Understanding Significant Figures in Measurements

Aug 20, 2024

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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