Question

Rational and irrational numbers quick check answers

Answer 1

Sure! Here’s a quick overview of rational and irrational numbers along with some examples:

### Rational Numbers:
- **Definition**: Numbers that can be expressed as the quotient or fraction \( \frac{a}{b} \) of two integers, where \( b \neq 0 \).
- **Examples**:
- \( \frac{1}{2} \) (0.5)
- \( -3 \) (which can be written as \( \frac{-3}{1} \))
- \( 0.75 \) (which is \( \frac{3}{4} \))
- \( 2 \) (which is \( \frac{2}{1} \))
- \( 0 \) (which can be written as \( \frac{0}{1} \))

### Irrational Numbers:
- **Definition**: Numbers that cannot be expressed as a simple fraction; their decimal expansions are non-repeating and non-terminating.
- **Examples**:
- \( \sqrt{2} \) (approximately 1.414)
- \( \pi \) (approximately 3.14159)
- \( e \) (approximately 2.718)
- \( \sqrt{3} \) (approximately 1.732)

### Quick Check:
1. Is \( 1.5 \) rational or irrational? **Rational**
2. Is \( \sqrt{5} \) rational or irrational? **Irrational**
3. Is \( -2/3 \) rational or irrational? **Rational**
4. Is \( 0.333... \) (repeating) rational or irrational? **Rational**
5. Is \( \sqrt{16} \) rational or irrational? **Rational** (since it equals 4)

If you have specific numbers you want to check or any other questions regarding rational and irrational numbers, feel free to ask!