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Rational and Irrational Numbers

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Rational and Irrational Numbers

Mathematical numbers and symbols illustration

📚 Part 1: Definitions and Classification

1. Complete the definitions:

Rational numbers: Numbers that can be expressed as a _________ where the numerator and denominator are _________ and the denominator ≠ _____.

Irrational numbers: Numbers that _________ be expressed as a fraction of integers. Their decimal expansions are _________ and _________.

2. Circle whether each number is RATIONAL or IRRATIONAL:

a) 3/4

Rational
Irrational

b) π (pi)

Rational
Irrational

c) 0.75

Rational
Irrational

d) √2

Rational
Irrational

e) -5

Rational
Irrational

f) 0.333...

Rational
Irrational

🔍 Part 2: Calculator Exploration

3. Use your calculator to find decimal approximations. Write the first 6 decimal places:

a) π ≈ 3.___________

b) √2 ≈ 1.___________

c) √3 ≈ 1.___________

4. Look at the decimal 0.142857142857142857... What pattern do you notice?
5. Is 0.142857142857... rational or irrational? Explain your reasoning:
6. Which of these statements about irrational numbers are true? Tick all that apply:

Their decimal expansions never end

They can be written as exact fractions

Their decimal expansions never repeat

√9 is an example of an irrational number

✏️ Part 3: Application and Reasoning

7. Explain why √9 is rational but √2 is irrational:
8. Sort these numbers into the correct categories by writing them in the appropriate box:

Numbers to sort: 2/3, √5, 0.25, π, -7, 0.666..., √16, 1.41421356...

Rational Numbers:

Irrational Numbers:

9. Create your own example of a rational number and explain why it's rational:
10. In one sentence, explain the key difference between rational and irrational numbers:

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