Understanding Real Numbers

Introduction to Real Numbers

• Real numbers can be understood using the number line.
• Positive numbers are located to the right of zero, while negative numbers are to the left.
• Simplest Definition: Any number that can be plotted on a number line is a real number.

Examples of Real Numbers

• -2: Can be plotted on the number line.
• 0.5: Not an integer, but can be plotted on the number line.
• √2 (Square Root of 2): Approximate value is 1.414.
  • This is a non-terminating decimal number.
• π (Pi): Approximately 3.14159.
  • Another example of a non-terminating decimal.

Types of Numbers

1. Terminating Decimals

   • Example: 0.375 (stops at a point)

2. Non-Terminating Recurring Decimals

   • Example: 0.6666... (the digit 6 occurs infinitely)

3. Non-Terminating Non-Recurring Decimals

   • Example: √2 (no specific pattern, digits after the decimal do not end)

Rational and Irrational Numbers

• Rational Numbers: Include terminating and recurring decimals.
• Irrational Numbers: Include non-terminating non-recurring decimals (e.g., √2, π).
• Definition of Real Numbers: Rational numbers and irrational numbers together form real numbers.

Conclusion

• In the second part of this video, we will explore all categories that real numbers comprise of.