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Rational and Irrational Numbers
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Rational and Irrational Numbers
📚 Part 1: Multiple Choice & Identification
1. Which of the following is an irrational number?
22/7
π
0.75
4
2. 0.333... (repeating) is rational because:
its decimal terminates
it can be written as a fraction
it is non-terminating and non-repeating
it equals √2
3. Check all that are rational numbers:
√9
0.121212... (12 repeating)
√2
5/8
4. Which decimal best describes a non-terminating, non-repeating decimal?
0.142857142857... (repeating)
0.1010010001... (pattern changes)
0.5
0.125
✏️ Part 2: Short Answer and Justify
5. Convert 0.\overline{72} (72 repeating) to a fraction. Show algebraic work.
6. Is √49 rational or irrational? Explain your reasoning using precise vocabulary (term, pattern, or fraction).
7. Order the following from least to greatest: 3, √5, 2.8, π. Show a brief justification (approximate values or reasoning).
8. Exit ticket — Answer both parts briefly:
a) Is 4.56789... with no repeating pattern rational or irrational? Why? _________
b) Give one example of a rational number and one example of an irrational number.
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