Rational vs. Irrational Numbers

Introduction

• Purpose: To differentiate between rational and irrational numbers.
• Method: Definitions, examples, and practice problems.

Definitions

Integer

• A number on a number line without fractions.
  • Examples: 0, 1, -1, -2, 2, etc.
• Integers go in both directions infinitely.

Rational Number

• Can be expressed as a ratio of two integers (a fraction).
  • Form: Integer in the numerator and integer in the denominator.
  • Example: 4/9, -2/5, 3/2.
• Includes terminating decimals and repeating decimals.
  • Terminating Decimals: Can be written as a ratio (e.g., 0.752 = 752/1000).
  • Repeating Decimals: Decimal that goes on forever but repeats (e.g., 0.333... = 1/3).

Irrational Number

• Cannot be expressed as a ratio of two integers.
• Decimals that neither terminate nor repeat.
  • Examples: π (pi = 3.14159…), e (2.71828…), √2.

Examples

Rational Numbers

• Whole Numbers: 8 can be expressed as 8/1.
• Terminating Decimals: 0.752, 0.125.
• Repeating Decimals: 0.333...
• Fractional Examples: 4/1 from √16.

Irrational Numbers

• π (Pi): 3.14159…
• e: 2.71828…
• Non-Simplifiable Square Roots: √2.

Square Roots

• Rational: √16 = 4 (can be simplified).
• Irrational: √8 (cannot be fully simplified).

Operations Involving Irrational Numbers

• Adding an irrational number (e.g., 7 + √8) leads to an irrational result.

Practice

• Task: Identify if given numbers are rational or irrational.
• Interaction: Post answers in comments for feedback.

Additional Resources

• Free printable notes available in description.
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Conclusion

• Recap of rational vs irrational.
• Encourage viewer participation and sharing the content.