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 times and 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 times and add zeros 7870000 Re-write number in standard form

Math Review [18(y^6)]/(x^4) 3(x^2)/4 x = -6 See Graph (-9, 5) Graphing Equations Linear Systems Current Unit 1. 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. [18(y^6)]/(x^4) See Graph (-9, 5) 3(x^2)/4 x = -6

Tuesday Math Review Exponents 1. Simplify the following expression: (a6b)(a3b2) Square Root Expressions / Equations 2. If x and y are positive, then simplify: Excluded Values 3. What are the excluded values of the expression? a9b3 12x6y5 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

Guided Practice

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. 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