📚 Part 1: Definitions and Understanding

1. Complete the definitions below:

Rational numbers are numbers that can be expressed as _________________ where the numerator and denominator are _________________ and the denominator ≠ _____.

Irrational numbers are 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

Rational

Irrational

c) 0.333...

Rational

Irrational

d) √2

Rational

Irrational

e) -7

Rational

Irrational

f) √9

Rational

Irrational

🔍 Part 2: Calculator Exploration

3. Use your calculator to find decimal approximations. Write the first 8 decimal places and describe the pattern:

a) π ≈ 3._________________ Pattern: _________________________________

b) √2 ≈ 1._________________ Pattern: _________________________________

c) √3 ≈ 1._________________ Pattern: _________________________________

4. Explain why 0.333... is rational even though it doesn't terminate:

5. Convert these fractions to decimals using your calculator. Do they terminate or repeat?

a) 1/8 = _________ (terminates / repeats)

b) 2/3 = _________ (terminates / repeats)

c) 5/6 = _________ (terminates / repeats)