Classifying Numbers

In this lesson, we'll classify numbers into different categories: Whole Numbers, Integers, Rational Numbers, and Irrational Numbers.

1. Whole Numbers

• Whole numbers are non-negative numbers without fractions or decimals.
• The set of whole numbers is: 0, 1, 2, 3, ...

2. Integers

• Integers include all whole numbers and their negative counterparts.
• The set of integers is: ..., -3, -2, -1, 0, 1, 2, 3, ...

3. Rational Numbers

• Rational numbers are numbers that can be expressed as the ratio of two integers, where the denominator is not zero.
• For example, $\frac{1}{2}$ and $-3$ are rational numbers.
• The set of rational numbers is: $\frac{a}{b}$, where $a$ and $b$ are integers and $b = 0$.

4. Irrational Numbers

• Irrational numbers cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions.
• Examples include $\sqrt{2}$ and $\pi$.

Example

Let's classify the number 4.5:

• Whole Number? No, because it has a decimal.
• Integer? No, because it is not a whole number.
• Rational? Yes, because it can be expressed as $\frac{9}{2}$.
• Irrational? No, because it can be expressed as a fraction.

Key Questions

• What is the difference between whole numbers and integers?
• Can all rational numbers be represented as decimals? Why or why not?
• Give an example of an irrational number.

Summary

• Whole Numbers: Non-negative integers (0, 1, 2, ...)
• Integers: Whole numbers and their negatives (..., -2, -1, 0, 1, 2, ...)
• Rational Numbers: Can be expressed as $\frac{a}{b}$ where $b = 0$
• Irrational Numbers: Cannot be expressed as a fraction, non-terminating decimals.

Understanding these number classifications helps us in various math concepts and applications.