OBJECTIVE

• I will write numbers that are in standard form in scientific notation.

• I will write numbers that are in scientific notation in standard form.

Vocabulary

• Scientific Notation - a number written as a product of a number and a power of ten

c x 10n

- c is a number greater than or equal to 1 and less than 10 (1 ≤ c < 10)

- n is any integer

Comparison of Forms

• Standard Form: 286000

• Product Form: 2.86 x 100000

• Scientific Notation: 2.86 x 105

Writing Numbers in Scientific Notation

• Step 1: Move the decimal so that it has one digit to the left of it greater than zero (if there is no decimal, write one at the end of the number)

• Step 2: Multiply the number by the place-value of the number of times the decimal moved (Product form)

• Step 3: Re-write the place-value as a power of ten (Scientific notation)

Writing Numbers in Scientific Notation

Joseph King constructed a 23 foot model of the Eiffel Tower using 110000 toothpicks. Write this number using scientific notation.

• Standard Form: 110000.Move the decimal 5 places to the left to make 1.1

Writing Numbers in Scientific Notation

• Product Form: 1.1 x 100000

• Scientific Notation: 1.1 x 105

• ANSWER Joseph King used 1.1 x 105 toothpicks to make his model of the Eiffel Tower.

5 zeros

Exponent is 5

Guided Practice

• Write 314700000 in Scientific notation.

314700000 Original Problem

3.147 Move decimal to the left 8 times

3.147 x 100000000 Multiply by place-value decimal moved

3.147 x 108 Re-write place-value as power of ten; Scientific notation

Writing Numbers in Standard Form

• Step 1: Remove the power of ten

• Step 2: Move the decimal to the right the number of places indicated by the exponent (if there is no decimal, add one)

• Step 3: Add zeros if the decimal goes beyond the number of digits

• Step 4: Re-write the number

Writing Numbers in Standard Form

Write 3 x 103 in standard form.

3.0 Add decimal

3000. Move decimal to right three timesand add zeros

3000 Re-write number in standard form

Guided Practice

Write 7.87 x 106 in standard form.

7870000. Move decimal to right three timesand add zeros

7870000 Re-write number in standard form

Math ReviewGraphing Equations Linear Systems Current Unit1. Graph the equation using 2. Solve the system of equations. 3. Find the product using the properties of the method of your choice. exponents.

Fraction Operations Multi-Step Equations

4. Evaluate. Reduce if necessary. 5. Solve for x.

(-9, 5)

x = -6

[18(y^6)]/(x^4)See Graph

3(x^2)/4

7 3 9x y

3

2

15 4

8 45

x x

x

6 63

4

x

2 4

14 11

2

x y

x y

3 6 2 87 5x y x y

Tuesday Math ReviewExponents1. Simplify the following expression:

(a6b)(a3b2)Square Root Expressions / Equations2. If x and y are positive, then simplify:

Excluded Values3. What are the excluded values of the

expression?

a9b3

12x6y5

x = -8

144x12y10

12

5(x 8)

OBJECTIVE

• I will compute problems with scientific notation using the rules of exponents.

Computing with Scientific Notation

• Step 1: Perform operation with numbers (c) and powers separately

• Step 2: Use properties of exponents

• Step 3: Simplify

• Step 4: Write in scientific notation

Multiplying with Scientific Notation

(2.2 x 102)(8.1 x 103) Problem

= (2.2 • 8.1) x (102 • 103) Multiply separately

= 17.82 x 105 Simplify

= 1.782 x 106 Write in scientific notation

Guided Practice

(4.5 x 104)(2.5 x 107)

Dividing with Scientific Notation

Problem

Divide separately

Simplify

Write in scientific

notation

1.5 10 2

7.5 10 8

1.5

7.5

10 2

10 8

0.2 106

2.0 105

Guided Practice

2.2 103

8.8 10 4

Powers with Scientific Notation

(1.2 x 102)3 Problem

= 1.23 x (102)3 Raise to power separately

= 1.728 x 106 Simplify

Guided Practice

(4.0 x 10-4)2

Independent Practice

Write the number in scientific notation.

1. 5480

Write the number in standard form.

2. 8.9 x 102

Compute the problem using scientific notation.

3. (1.25 x 103)(3.5 x 102)

4. (1.25 x 103)4