Elimination Using Multiplication
Prime Factors
Equations Involving Rational Exponents
Working with Percentages and Proportions
Rational Expressions
Interval Notation and Graphs
Simplifying Complex Fractions
Dividing Whole Numbers with Long Division
Solving Compound Linear Inequalities
Raising a Quotient to a Power
Solving Rational Equations
Solving Inequalities
Adding with Negative Numbers
Quadratic Inequalities
Dividing Monomials
Using the Discriminant in Factoring
Solving Equations by Factoring
Subtracting Polynomials
Cube Root
The Quadratic Formula
Multiply by the Reciprocal
Relating Equations and Graphs for Quadratic Functions
Multiplying a Polynomial by a Monomial
Calculating Percentages
Solving Systems of Equations using Substitution
Comparing Fractions
Solving Equations Containing Rational Expressions
Factoring Polynomials
Negative Rational Exponents
Roots and Radicals
Intercepts Given Ordered Pairs and Lines
Factoring Polynomials
Solving Linear Inequalities
Mixed Expressions and Complex Fractions
Solving Equations by Multiplying or Dividing
The Addition Method
Finding the Equation of an Inverse Function
Solving Compound Linear Inequalities
Multiplying and Dividing With Square Roots
Exponents and Their Properties
Equations as Functions
Factoring Trinomials
Solving Quadratic Equations by Completing the Square
Dividing by Decimals
Lines and Equations
Simplifying Complex Fractions
Graphing Solution Sets for Inequalities
Standard Form for the Equation of a Line
Checking Division with Multiplication
Elimination Using Addition and Subtraction
Complex Fractions
Multiplication Property of Equality
Solving Proportions Using Cross Multiplication
Product and Quotient of Functions
Quadratic Functions
Solving Compound Inequalities
Operating with Complex Numbers
Equivalent Fractions
Changing Improper Fractions to Mixed Numbers
Multiplying by a Monomial
Solving Linear Equations and Inequalities Graphically
Dividing Polynomials by Monomials
Multiplying Cube Roots
Operations with Monomials
Properties of Exponents
Mixed Numbers and Improper Fractions
Equations Quadratic in Form
Simplifying Square Roots That Contain Whole Numbers
Dividing a Polynomial by a Monomial
Writing Numbers in Scientific Notation
Solutions to Linear Equations in Two Variables
Solving Linear Inequalities
Multiplying Two Mixed Numbers with the Same Fraction
Special Fractions
Solving a Quadratic Inequality
Parent and Family Graphs
Solving Equations with a Fractional Exponent
Evaluating Trigonometric Functions
Solving Equations Involving Rational Expressions
Laws of Exponents
Multiplying Polynomials
Vertical Line Test
Solving Inequalities with Fractions and Parentheses
Multiplying Polynomials
Solving Quadratic and Polynomial Equations
Extraneous Solutions
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Writing Numbers in Scientific Notation

There are two steps to writing a large positive number in scientific notation. Consider the number 1,649,000,000. The first step is to move the decimal point to the right of the leftmost digit. Remove all of the zeros on the far right.

The second step is to multiply this number by a power of 10. To find the power of 10, count the number of places you moved the decimal point.

So, in scientific notation, 1,649,000,000 is written 1.649 ×10 9.


Example 1

Write 3,587,000,000,000 in scientific notation.


3,587,000,000,000 = 3.587 ×10 12 Move the decimal point 12 places to the left. Multiply by 10 12.

To write numbers less than 1 in scientific notation, there is a similar method. Consider the number 0.0000387. The first step is to move the decimal point to the right of the first nonzero digit. Remove all of the zeros on the far left.

The second step is to multiply this number by a power of 10. To find the power of 10, count the number of places you moved the decimal point. Then use the negative of that number as the exponent of 10.

In this case, the decimal point was moved 5 places. So, -5 will be used as the exponent of ten. In scientific notation, 0.0000387 is written 3.87 ×10 -5.


Example 2

Write 0.000000634 in scientific notation.


0.000000634 = 6.34 ×10 -7 Move the decimal point 7 places to the right. Multiply by 10 -7.


Comparing and Ordering Numbers in Scientific Notation

It is easy to compare two numbers that are given in scientific notation.

Key Idea

To compare two numbers given in scientific notation, first compare the exponents. The one with the greater exponent will be greater. If the exponent is the same, compare the two numbers that are being multiplied by comparing their decimals.


Example 3

Compare 6.23 × 10 14 and 8.912 × 10 12 .


Since the exponent in the first number is greater than the exponent in the second number, 6.23 × 10 14 is greater than 8.912 × 10 12.


Example 4

Which is greater, 5.15 × 10 -4 or 6.35 × 10 -5 ?


Since -4 is greater than -5, 5.15 × 10 -4 is greater than 6.35 × 10 -5 .


Example 5

Compare 3.28 × 10 17 and 4.25 × 10 17 .


The exponents are both 17. So, we need to compare the numbers that are being multiplied. Since 4.25 is greater than 3.28, 4.25 × 10 17 is greater than 3.28 × 10 17 .

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