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Rational and Irrational Numbers

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Rational and Irrational Numbers

Number line with rational and irrational numbers

📚 Part 1: Number Classification

1. Which of the following is a rational number?

√2

π

3/4

√5

2. The decimal 0.333... (repeating) is:

Rational

Irrational

Neither

Cannot be determined

3. Which numbers are irrational? (Check all that apply)

√9

√7

0.75

π

-2/3

4. The number 0.125 can be written as the fraction:

1/8

1/4

3/8

5/8

✏️ Part 2: Justification and Reasoning

5. Explain why √16 is a rational number, but √15 is irrational.
6. Complete the statement: A rational number is any number that can be expressed as _________, where the denominator is not _________.
7. Look at the decimal 0.121212... (repeating pattern "12")

a) Is this number rational or irrational? _____________

b) Justify your answer:

8. Place these numbers in the correct category by writing them in the boxes below:

Numbers: 2/5, √3, 0.666..., π, -7, √25, 0.5

Rational Numbers:

Irrational Numbers:

🎯 Part 3: Problem Solving

9. A student claims that all square roots are irrational numbers. Do you agree or disagree? Give two examples to support your answer.
10. On the number line below, mark the approximate locations of √2, 1.5, and π.

Number line from 0 to 4:

0 _____|_____|_____|_____|_____|_____|_____|_____ 4

1 2 3

11. Real-world connection: A pizza costs $12.99. Is this price a rational or irrational number? Explain how you know.

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