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 placevalue 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
5 zeros
• Scientific Notation: 1.1 x 105
Exponent is 5
• ANSWER Joseph King used 1.1 x 105
toothpicks to make his model of the
Eiffel Tower.
Guided Practice
• Write 314700000 in Scientific notation.
314700000
3.147
Original Problem
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
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.
x  2 y  4
1
x  4 y  11
2
7x  3y  9
See Graph
(-9, 5)
Fraction Operations
4. Evaluate. Reduce if necessary.
3
15 x 4 x

8 45 x 2
3(x^2)/4
7 x y  5x y
3
6
2
8
[18(y^6)]/(x^4)
Multi-Step Equations
5. Solve for x.
6x  6
 3
4
x = -6
Tuesday Math Review
Exponents
1. Simplify the following expression:
(a6b)(a3b2)
a9b3
Square Root Expressions / Equations
2. If x and y are positive, then simplify:
12x6y5
144x12 y10
Excluded Values
3. What are the excluded values of the
expression? 12
x = -8
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)
= (2.2 • 8.1) x (102 • 103)
= 17.82 x 105
= 1.782 x 106
Problem
Multiply separately
Simplify
Write in scientific notation
Guided Practice
(4.5 x 104)(2.5 x 107)
Dividing with Scientific
Notation
1.5  102
8
7.5  10
2
1.5 10

 8
7.5 10
6
 0.2  10
 2.0  10
Problem
Divide separately
Simplify
5
Write in scientific
notation
Guided Practice
2.2  10
4
8.8  10
3
Powers with Scientific
Notation
(1.2 x 102)3
= 1.23 x (102)3
= 1.728 x 106
Problem
Raise to power separately
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