Introduction to Real Numbers

Year 9 Mathematics Understanding Number Classification Lesson 1 of 4

WALT - We Are Learning To

Understand the definition of real numbers Distinguish between rational and irrational numbers Place numbers on a number line Provide examples of each type of number

Quick Review: What Numbers Do You Know?

Think about different types of numbers you've learned Natural numbers, whole numbers, integers... Can you give examples of each?

The Real Number System Hierarchy

Rational Numbers

Can be written as a fraction a/b where b ≠ 0 Include all integers, fractions, and terminating decimals Examples: 3/4, -5, 0.5, 0.333... (repeating) Their decimal form either terminates or repeats

Irrational Numbers

Cannot be written as a simple fraction Decimal expansions never end and never repeat Examples: π (pi), √2, √3, e (Euler's number) Found in geometry, nature, and advanced mathematics

Number Line Classification Activity

Receive your number cards Classify each number as rational or irrational Place them correctly on your number line Discuss with your partner

Remember

Real Numbers = Rational Numbers + Irrational Numbers Every number you can think of is a real number! The key is knowing which type it is