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Scientific Notation
Notation and Symbols
Linear Equations and Inequalities in One Variable
Graphing Equations in Three Variables
What the Standard Form of a Quadratic can tell you about the graph
Simplifying Radical Expressions Containing One Term
Adding and Subtracting Fractions
Multiplying Radical Expressions
Adding and Subtracting Fractions
Multiplying and Dividing With Square Roots
Graphing Linear Inequalities
Absolute Value Function
Real Numbers and the Real Line
Monomial Factors
Raising an Exponential Expression to a Power
Rational Exponents
Multiplying Two Fractions Whose Numerators Are Both 1
Multiplying Rational Expressions
Building Up the Denominator
Adding and Subtracting Decimals
Solving Quadratic Equations
Scientific Notation
Like Radical Terms
Graphing Parabolas
Subtracting Reverses
Solving Linear Equations
Dividing Rational Expressions
Complex Numbers
Solving Linear Inequalities
Working with Fractions
Graphing Linear Equations
Simplifying Expressions That Contain Negative Exponents
Rationalizing the Denominator
Estimating Sums and Differences of Mixed Numbers
Algebraic Fractions
Simplifying Rational Expressions
Linear Equations
Dividing Complex Numbers
Simplifying Square Roots That Contain Variables
Simplifying Radicals Involving Variables
Compound Inequalities
Factoring Special Quadratic Polynomials
Simplifying Complex Fractions
Rules for Exponents
Finding Logarithms
Multiplying Polynomials
Using Coordinates to Find Slope
Variables and Expressions
Dividing Radicals
Using Proportions and Cross
Solving Equations with Radicals and Exponents
Natural Logs
The Addition Method
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Notation and Symbols

You have used many different notations and symbols in your study of mathematics, including exponential notation and ordering symbols. Here are some examples for you to review.

A positive integer exponent is used to indicate repeated multiplication of a number.

For example, the expression 73 is written in exponential notation. It means 7 · 7 · 7. The exponent is 3 and the base is 7.

Ordering symbols are used to indicate the relative position of two numbers on a number line. The number on the left is less than the number on the right.

For example, -4 is less than 2 because -4 lies to the left of 2.

Symbol Meaning Example Position on Number line
= is equal to Same position.
is not equal to -4 ≠ 2 Different position.
< is less than -4 < 2 -4 is to the left of 2.
> is greater than 2 > -4 2 is to the right of -4.
is less than or equal to -4 ≤ 2

-4 ≤ -4

-4 is to the left of 2.

Same position.

is greater or equal to 2 ≥ -4

-4 ≥ -4

- is to the right of -4.

Same position.


The pointed end of the inequality symbol always points towards the smaller number.

Thus, “four is less than seven” is written 4 < 7.

Likewise, “seven is greater than four” is written 7 > 4.

Example 2

Which of the following statements are true?

a. -6 > -2

b. -5 < 3

c. 7 7


a. False. -6 > -2 is read “negative six is greater than negative two.” This statement is false because -6 lies to the left of -2 on the number line. Therefore, -6 < -2.

b. True. -5 < 3 is read “negative five is less than three.”

This is true because -5 lies to the left of 3 on the number line.

c. True. 7 7 is read “seven is less than or equal to 7.” This means either “7 is less than 7” or “7 is equal to 7.” Since 7 = 7, the statement 7 7 is true. (An “or” statement is true if either part is true.)

Note: The statement 7 ≥ 7 is also true.

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