Classifying Real Numbers Practice

Classifying Real Numbers:

1. The Natural Numbers start with 1 and then increase by 1 indefinitely
   • {1, 2, 3, ...}
2. The Whole Numbers are the Natural Numbers with the inclusion of 0
   • {0, 1, 2, 3, ...}
3. The Integers contain all Whole Numbers and their opposites
   • {... , -3, -2, -1, 0, 1, 2, 3, ...}
4. The Rational Numbers contain all numbers that can be expressed as the quotient of two integers, where the denominator is not zero
   • {p/q | p and q are integers, q ≠ 0}
   • Rational Numbers have decimals that terminate or repeat the same pattern indefinitely
   • Ex: 1/4 = 0.25
   • Ex: 4/11 = 0.36
5. The Irrational Numbers contain all real numbers that are not Rational Numbers
   • {x | x is a real number that is not a rational number}
   • Decimal numbers that don't terminate or repeat the same pattern
   • Square roots of non-perfect squares
   • Ex: π (pi is the ratio of the circumference of a circle to its diameter)
   • Ex: √2 (2 is not a perfect square, so the square root of 2 is irrational)

Step-by-Step: