Dr. Algebra

Number Types and Groups

Numbers are often lumped together in groups, or classes, for easy reference.  Most numbers will fall into multiple groups as listed below:

  • Natural — Positive numbers that don’t have fractions:  ( 1, 2, 3, 4, 5, 6, and so on forever).

  • Whole — Natural numbers PLUS zero: ( 0, 1, 2, 3, 4, 5, 6, . . . and so on forever)
    • No negative numbers
    • Note the three dots indicate the list of numbers continues on.

  • Integers — Whole numbers PLUS the matching set of negative numbers:
    • ( . . . , -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, . . .)
    • Note there are NO FRACTIONS or DECIMALS.
  • Prime — A number is PRIME if it is a natural number that can ONLY be divided by the number ‘1’ and itself. 
    • (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, . . .)
    • 1 is not generally considered prime.
  • Rational. Integers and other numbers that can be written out as a fraction.
    • Examples: \(\color{Red}3.67, \frac{5}{7}, 1/2, \frac{1}{3}, 5.31111111…,\)

  • Irrational. Those numbers that cannot be expressed as a fraction.
    • Examples:
      • [katex]\color{Red}\sqrt{2}[/katex]
      • [katex]\color{Red}\sqrt{2}[/katex]
    • These numbers do NOT repeat
    •  
  • Real numbers — The set of all integers plus fractions of numbers.

  • Complex and/or Imaginary numbers — These involve the \(\sqrt{-1}\) and further information information can be found on the complex numbers page.  
  • Click HERE for a VIDEO of this Lesson
  • Click HERE for VIDEO Examples
  • Click HERE for a worksheet with problems

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