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Rational Irrational Numbers Worksheet

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Rational and Irrational Numbers Worksheet

Mathematical symbols and numbers illustration

📚 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)

✏️ Part 3: Quick Quiz

6. For each number below, identify if it's rational or irrational AND justify your answer:

a) 0.75

Type: _________________ Justification: _________________________________


b) √5

Type: _________________ Justification: _________________________________


c) 22/7

Type: _________________ Justification: _________________________________


d) 0.121212...

Type: _________________ Justification: _________________________________


e) √16

Type: _________________ Justification: _________________________________

7. In your own words, explain the main difference between rational and irrational numbers. Give one example of each:

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