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Introduction

This tutorial provides a comprehensive guide on significant figures, rounding rules, and their operations, specifically designed for high school students. Understanding significant figures is crucial for accurate measurements and calculations in physics and mathematics. This step-by-step guide will help you master the concepts and rules associated with significant figures.

Step 1: Understanding Significant Figures

• Significant figures are the digits in a number that contribute to its precision.
• All non-zero digits are considered significant.
• Zeros:
  • Leading zeros (e.g., 0.0025) are not significant.
  • Captive zeros (e.g., 1002) are significant.
  • Trailing zeros in a decimal (e.g., 2.500) are significant, while in a whole number without a decimal (e.g., 2500) they may or may not be significant depending on context.

Step 2: Rules for Rounding Significant Figures

• When rounding numbers, follow these guidelines:
  • If the digit to the right of the last significant figure is less than 5, round down.
  • If the digit is 5 or greater, round up.
• Examples:
  • Rounding 2.345 to three significant figures results in 2.35.
  • Rounding 6857.35 to three significant figures results in 6857.45. (Corrected example from the video)

Step 3: Operations with Significant Figures

• When performing calculations, the precision of your result should reflect the precision of the least precise measurement.
• Follow these specific rules for different operations:

Addition and Subtraction

• The result should be reported to the same number of decimal places as the measurement with the least decimal places.
• Example:
  • 12.11 (2 decimal places) + 0.3 (1 decimal place) = 12.41 (rounded to 12.4).

Multiplication and Division

• The result should have the same number of significant figures as the measurement with the least significant figures.
• Example:
  • 52.731 (5 significant figures) × 7.20 (3 significant figures) = 379.6632 (rounded to 380, which has 3 significant figures).

Step 4: Powers and Roots with Significant Figures

• When raising a number to a power or taking a root, the result should be rounded according to the significant figures of the original number.
• For example:
  • If you have 2.5², which has 2 significant figures, the result is 6.25 but should be reported as 6.3.

Step 5: Scientific Notation and Significant Figures

• In scientific notation, all digits in the coefficient are significant.
• Example:
  • 4.500 × 10³ has 4 significant figures.
  • Be careful with the exponent; it does not affect the number of significant figures.

Conclusion

Understanding significant figures is essential for accurate calculations in science and mathematics. Remember the rules for identifying significant figures, rounding, and performing mathematical operations. Practice these concepts regularly to improve your skills. For further study, consider practicing with different examples or exploring more complex scenarios involving significant figures.