Rational and Irrational Numbers

Name:

Date:

📚 Part 1: Multiple Choice & Identification

1. Which of the following is an irrational number?

22/7

0.75

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

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.