Order of Real Numbers

Key Questions

  • How do you classify real numbers?

    Answer:

    Irrational and rational numbers
    Rational numbers: integers, whole numbers, counting/natural numbers

    Explanation:

    Real numbers are either irrational or rational. Rational numbers can be written as fractions (using two integers, such as #4/5# or #-6/3#). Terminating decimals and repeating decimals are examples of rational numbers.

    Rational numbers: #3, -9, 12, -777, 0.3bar3, 12/7, 0.46, 0.16bar6#

    Irrational numbers: #sqrt2, sqrt3, sqrt5, 2sqrt3, -sqrt13, pi#

    There are several different groups of rational numbers. There are integers, whole numbers, and counting/natural numbers. Integers do not have decimals. They can be positive or negative.

    Integers: #6, 16, -72, 89, 23, -1, 0#

    Whole numbers are all non-negative integers. Examples include #16, 0, 23, 45559#.

    Natural/counting numbers are all positive integers. (We don't start counting from zero).

    Counting numbers: #1, 2, 3, 4, 5...#

    Serena D. · 1 · Apr 16 2018
  • How do you compare real numbers?

    You can either compare their decimal representations or compute the difference to see if it is positive or negative.

    Example 1

    #pi=3.14...#

    #2sqrt(3)=3.46...#

    Hence, #pi < 2sqrt{3}#.

    Example 2

    #2sqrt(2)-e=0.11...>0#

    Hence, #2sqrt{2} > e#

    I hope that this was helpful.

    Wataru · 2 · Nov 9 2014
  • What are Real Numbers?

    You can think of a real number as a number that has a decimal representation including the ones having infinitely many digits.

    I hope that this was helpful.

    Wataru · 1 · Oct 26 2014

Questions

Properties of Real Numbers