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Rational Irrational Numbers Worksheet
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Rational and Irrational Numbers Worksheet
📚 Part 1: Multiple Choice
1. Which of the following is the best definition of a rational number?
A number that makes sense
A number that can be expressed as a fraction where both numerator and denominator are integers (denominator ≠ 0) (Correct Answer)
A positive number only
A number without decimals
2. Which number is irrational?
0.75
-4
√2 (Correct Answer)
1/3
3. The decimal expansion 0.333... is:
Rational because it repeats (Correct Answer)
Irrational because it never ends
Neither rational nor irrational
Impossible to determine
4. Which of these numbers are rational? (Select all that apply)
√9 (Correct Answer)
π
0.142857... (Correct Answer)
5 (Correct Answer)
√3
🔗 Part 2: Matching Activity
5. Match each number to its correct classification:
3/4 (Rational)
√2 (Irrational)
-7 (Rational)
π (Irrational)
0.25 (Rational)
Rational
Irrational
Rational
Irrational
Rational
✏️ Part 3: Short Answer Questions
6. Explain why √16 is rational but √17 is irrational.
√16 = 4, which is a whole number (rational). √17 is not a whole number and cannot be expressed as a fraction (irrational).
7. A student claims that all decimals are irrational because "they have decimal points." Explain why this statement is incorrect and give an example.
Not all decimals are irrational; for example, 0.5 is a terminating decimal and can be expressed as 1/2 (rational).
8. Complete the following sentences:
a) A rational number can always be written as p/q where both parts are integers.
b) An irrational number has a decimal expansion that is non-terminating and non-repeating.
9. Use your calculator to find the decimal approximation of √5. Based on what you observe, classify this number as rational or irrational and explain your reasoning.
√5 ≈ 2.236, which is non-terminating and non-repeating (irrational).
10. Give two examples of rational numbers and two examples of irrational numbers. For each rational number, show how it can be written as a fraction.
Examples of rational numbers: 1/2 (0.5) and 3 (3/1). Examples of irrational numbers: √2 and π.
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