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Exponential Decay
Negative Exponents
Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
Solving Absolute Value Inequalities
Multiplying Special Polynomials
FOIL Method
Inequalities
Solving Systems of Equations by Graphing
Graphing Compound Inequalities
Solving Quadratic Equations by Completing the Square
Addition Property of Equality
Square Roots
Adding and Subtracting Fractions
The Distance Formula
Graphing Logarithmic Functions
Fractions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
Powers
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
Evaluating Polynomials
Slope
Angles and Degree Measure
   
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Exponents and Powers of Ten

To write one million as a numeral takes a 1 and six 0’s: 1,000,000. To write one billion, you use a 1 and nine 0’s: 1,000,000,000. One trillion is even larger and uses three more 0’s: 1,000,000,000,000.

Large numbers have always been interesting to mathematicians. Writing lots of zeros is not so interesting. There is a way to write abbreviations for large numbers, without all those pesky zeros!

- One million (1,000,000) can be written 106.

- One billion (1,000,000,000) can be written 109.

- One trillion (1,000,000,000,000) can be written 1012.

The little number is the same as the number of zeros, and is called an exponent. An exponent tells how many times to multiply the other number, called the base, by itself. So 106 equals 10 × 10 × 10 × 10 × 10 × 10, and that equals 1,000,000. (You can check this on your calculator.)

To read a power of ten, such as 1,000, you can say “one thousand” or “ten to the third power.” One million is “ten to the sixth power.”

With numbers that aren’t exactly a power of ten, 13 million (13,000,000) for example, mathematicians use shorthand that still uses exponents with ten as the base. Since 13 million is 13 times 1 million, you can write it as 13 × 106. That’s a standard abbreviation called scientific notation.

Exponents are especially useful when the powers of ten get even bigger. Here’s a chart that shows how handy mathematical shorthand can be.

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