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Solving Quadratic Equations by Completing the Square
Graphing Logarithmic Functions
Division Property of Exponents
Adding and Subtracting Rational Expressions With Like Denominators
Rationalizing the Denominator
Multiplying Special Polynomials
Functions
Solving Linear Systems of Equations by Elimination
Solving Systems of Equation by Substitution and Elimination
Polynomial Equations
Solving Linear Systems of Equations by Graphing
Quadratic Functions
Solving Proportions
Parallel and Perpendicular Lines
Simplifying Square Roots
Simplifying Fractions
Adding and Subtracting Fractions
Adding and Subtracting Fractions
Solving Linear Equations
Inequalities in one Variable
Recognizing Polynomial Equations from their Graphs
Scientific Notation
Factoring a Sum or Difference of Two Cubes
Solving Nonlinear Equations by Substitution
Solving Systems of Linear Inequalities
Arithmetics with Decimals
Finding the Equation of an Inverse Function
Plotting Points in the Coordinate Plane
The Product of the Roots of a Quadratic
Powers
Solving Quadratic Equations by Completing the Square

Scientific Notation

After studying this lesson, you will be able to:

  • Convert standard notation to scientific notation.
  • Convert scientific notation to standard notation

Standard Notation is the "normal" way of writing a number.

Example: 45,800

Example: 0.034

Scientific Notation is the way of writing a number as the product of a power of 10 and a number between 1 and 10. Scientific notation is often used to express very large numbers (using positive exponents) or very small numbers (using negative exponents.)

Example: 4.58 × 10 4

Example: 3.4 × 10 -2

 

Example 1

Write 1.25 × 10 3 in standard notation.

To convert we move the decimal the same number of places as the exponent. Since multiplying by 10 3 is the same as multiplying by 1000, we can just move the decimal three places to the right. (Hint: if we have positive exponents, we move the decimal to the right because we are multiplying.)

1.25 × 10 3 will be 1250 (we moved the decimal 3 places to the right)

 

Example 2

Write 7 × 10 5 in standard notation.

To convert we move the decimal the same number of places as the exponent. Since multiplying by 10 5 is the same as multiplying by 100,000, we can just move the decimal five places to the right.

7 × 10 5 will be 700,000 (we moved the decimal 5 places to the right)

 

Example 3

Write 4.8 x 10 -3 in standard notation.

To convert we move the decimal the same number of places as the exponent. Multiplying by a negative power of 10 is the same as dividing by that power of ten. Since multiplying by 10 -3 is the same as dividing by 1000, we can just move the decimal five places to the left. (Hint: if we have negative exponents, we move the decimal to the left because we are dividing.)

4.8 × 10 -3 will be .0048 (we moved the decimal 3 places to the left)

 

Example 4

Write 1.8 × 10 -4 in standard notation.

To convert we move the decimal the same number of places as the exponent. Multiplying by a negative power of 10 is the same as dividing by that power of ten. Since multiplying by 10 -4 is the same as dividing by 10000, we can just move the decimal four places to the left. (Hint: if we have negative exponents, we move the decimal to the left because we are dividing.)

1.8 × 10 -4 will be .00018 (we moved the decimal 4 places to the left)

 

Example 5

Write 12,450 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 12,450 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 1 and the 2. That means we moved the decimal 4 places to the left. Now, we write the product of 1.245 and a power of 10. Our power of 10 will be 3 since we moved the decimal 3 places . (Hint: when we are converting numbers greater than 1 we use positive exponents. Numbers less than 1 use negative exponents.)

12,450 will be 1.245 × 10 3 (we moved the decimal 3 places to the left)

 

Example 6

Write 139,000 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 139,000 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 1 and the 3. That means we moved the decimal 5 places to the left. Now, we write the product of 1.39 and a power of 10. Our power of 10 will be 5 since we moved the decimal 5 places .

139,000 will be 1.39 × 10 5 (we moved the decimal 5 places to the left)

 

Example 7

Write 0.2362 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 0.2362 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 2 and the 3. That means we moved the decimal 1 place to the right. Now, we write the product of 2.362 and a power of 10. Our power of 10 will be -1 since we moved the decimal 1 place . (Hint: when we are converting numbers less than 1 we use negative exponents.)

0.2362 will be 2.362 × 10 -1 (we moved the decimal 1 place to the right) ?

 

Example 8

Write 0.02004 in scientific notation. When converting from standard notation to scientific notation, the first thing we do is to move the decimal in 0.02004 to a point that the new number will be between 1 and 10. That means we need to move the decimal to where it is between the 2 and the 0. That means we moved the decimal 2 places to the right. Now, we write the product of 2.004 and a power of 10. Our power of 10 will be -2 since we moved the decimal 2 places . (Hint: when we are converting numbers less than 1 we use negative exponents.)

0.02004 will be 2.004 × 10 -2 (we moved the decimal 2 places to the right)

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