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Rational Irrational Numbers Worksheet

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Rational Irrational Numbers Worksheet

Mathematical symbols and numbers illustration

📚 Part 1: Classification

1. Circle whether each number is rational or irrational:

a) 3/4     Rational   Irrational

b) √2     Rational   Irrational

c) 0.333...     Rational   Irrational

d) π     Rational   Irrational

e) -7     Rational   Irrational

2. Which of the following are characteristics of rational numbers? Tick all that apply:

Can be expressed as a fraction where both numerator and denominator are integers

Have non-terminating, non-repeating decimal expansions

Include all integers

Include terminating decimals like 0.75

Include repeating decimals like 0.666...

3. Which number is irrational?

√9

√16

√5

0.25

🔍 Part 2: Analysis and Explanation

4. Complete the table by placing each number in the correct column:

Numbers to classify: 2/3, √7, 0.142857..., π, -5, 0.8, √25

5. Explain why 0.333... is a rational number, but √2 is irrational:
6. A student claims that all square roots are irrational numbers. Is this statement correct? Give examples to support your answer:
7. Use a calculator to find the decimal approximation of √3 to 6 decimal places. Based on this, explain why √3 is classified as irrational:

√3 ≈ ________________

✏️ Part 3: Application

8. Convert these fractions to decimals and determine if they terminate or repeat:

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

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

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

9. Give one example of each type of number and explain your reasoning:

Rational number: ________________

Irrational number: ________________

10. Challenge: Between which two consecutive integers does √10 lie? Show your reasoning using perfect squares:

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