1.2 Rational and Irrational Numbers

• Natural number - smallest

  Whole number - after natural

  Integers - after whole

  Rational number - biggest

  
  

  Irrational number - outside the circle
• Number System

  • how you group the numbers
• Natural numbers

  • all positive integers from 1 to infinity and there is no zero included
• Whole numbers

  • any number between zero to infinity, not including decimals or fractions
• Integers

  • both positive and negative numbers
• Rational numbers

  • can be written as fractions
  • recurring decimal
  • terminating decimal (does not repeat) ex: 0.7238
  • the square/cube root of a square/cube number is rational ex: √125 cube root is 5, so 5 is a rational number
  • important: all whole no. are rational, but not all rational numbers are whole no. cuz there are decimals and fractions in rational numbers
• Irrational numbers

  • cannot be written as fraction
  • square/cube root that is not a square/cube no. ex: √3 is not a square number
• Examples of rational numbers:

  • recurring - 0.7777777
  • terminating - 0.17
  • integers - -7/1
  • mixed fractions - 3 1/3
• Irrational fractions (can happen)

  • the numerator and denominator cannot be both integers
  • meaning one has to be a decimal