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:
- Is \( 1.5 \) rational or irrational? Rational
- Is \( \sqrt{5} \) rational or irrational? Irrational
- Is \( -2/3 \) rational or irrational? Rational
- Is \( 0.333... \) (repeating) rational or irrational? Rational
- 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!