Order of Real Numbers
Key Questions

Answer:
Irrational and rational numbers
Rational numbers: integers, whole numbers, counting/natural numbersExplanation:
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 nonnegative 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...# 
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.

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.
Questions
Properties of Real Numbers

Properties of Rational Numbers

Additive Inverses and Absolute Values

Addition of Integers

Addition of Rational Numbers

Subtraction of Rational Numbers

Multiplication of Rational Numbers

Mixed Numbers in Applications

Expressions and the Distributive Property

When to Use the Distributive Property

Division of Rational Numbers

Applications of Reciprocals

Square Roots and Irrational Numbers

Order of Real Numbers

Guess and Check, Work Backward