Download Scientific Notation

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Master Alabama’s 15 most challenging mathematics skills with
SkillBridge. With lesson topics chosen based on actual state test
data, SkillBridge offers help in the skills that truly are the most
troublesome. As students move through each lesson, they are
equipped with guidance and connections that allow them to show
independent skill mastery by the end of the lesson. Alabama
references in each lesson offer a unique and familiar
point of entry into difficult skills.
Mathema
tics
Alabama’s 15 most challenging skills
in mathematics, grade 8
• Scientific Notation
• Calculating Angle Measures
• Problem Solving
• Pythagorean Theorem
• Solving Equations
• Similar Figures
• Proportions
• Surface Area
• Functions
• Volume
• Slope
• Central Tendency
• Identifying Angle Pairs
• Probability
• Angle Pairs
Cochrane Bridge in Mobile, Alabama
Catalog Number ALB2068W1
P.O. Box 2180
Iowa City, Iowa 52244-2180
ISBN 978-0-7836-6302-9
50599
STUDENT NAME
PHONE: 800-776-3454
FAX: 877-365-0111
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Table of Contents
Scientific Notation (2.1)............................................................ 4
Problem Solving (1)................................................................. 8
Solving Equations (6)............................................................ 12
Proportions (1.3)..................................................................... 16
Functions (5, 5.1, 5.2)................................................................. 20
Slope (4.2). .............................................................................. 24
Identifying Angle Pairs (9).................................................... 28
Angle Pairs (9). ...................................................................... 32
Calculating Angle Measures (9)........................................... 36
Pythagorean Theorem (7, 7.3, 7.4)............................................ 40
Similar Figures (12, 12.1).......................................................... 44
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Surface Area (11, 11.3).............................................................. 48
Volume (11, 11.3)........................................................................ 52
Central Tendency (13.4).......................................................... 56
Probability (14.3)..................................................................... 60
2.1
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At the beginning of each lesson, you will see a box with the shape of
Alabama and a content standard code in it. This code tells you what is
being covered in the lesson
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2.1
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Scientific Notation
A power of 10 is a positive or negative exponent
that has a base of 10.
Powers of 10
101 � 10
–
10 1 � 0.1
102 � 100
–
10 2 � 0.01
103 � 1,000
–
10 3 � 0.001
and so on . . .
and so on . . .
Thirty Alabama colleges have
science degree programs.
Students sometimes view
particles so small that they
use scientific notation to
describe their size.
Scientific notation is a way to write very large or very small numbers. A number
written in scientific notation is a number between 1 and 10 that is multiplied by a
power of 10. The table below shows two examples.
Standard Notation
Scientific Notation
5,340,000
5.34 � 106
0.00016
1.6 � 10�4
To change a number from standard to scientific notation, follow these steps:
Step 2: Count the number of places you moved the decimal point. That number is
the power of 10. If you moved the decimal point to the left, the power of 10 is
positive. If you moved the decimal point to the right, the power of 10 is negative.
Step 3: Write the decimal from Step 1 multiplied by the power of 10 from Step 2.
Example 1
Write 4,800,000 in scientific notation.
Build A Bridge 1
First, move the decimal point 6 places to the left
so you have a number that is between 1 and 10.
Write 13,500 in scientific
notation.
4.800000.
Because you moved the decimal point to the left,
the power of 10 is positive. Now write the decimal
multiplied by the power of 10.
4,800,000 5 4.8 3 106
AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
Step 1: Move the decimal point to the left or right until you have a number greater
than or equal to 1 and less than 10.
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Example 2
Write 0.00672 in scientific notation.
Build A Bridge 2
Move the decimal point 3 places to the right.
Write 0.000008 in
scientific notation.
0.006.72
Because you moved the decimal point to the right,
the power of 10 is negative.
0.00672 5 6.72 3 1023
To change a number from scientific to standard notation, follow these steps:
Step 1: Look at the exponent to see how many places to move the decimal point.
Step 2: M
ove the decimal point to the right for a positive power of 10 or to the left
for a negative power of 10.
Step 3: Add zeros as placeholders where necessary.
Example 3
Write 5.12 3 104 in standard notation.
AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
The exponent is positive, so move the decimal
point 4 places to the right and add two zeros as
placeholders.
Build A Bridge 3
Write 1.906 3 107 in
standard notation.
5.1200.
5.12 3 104 5 51,200
Example 4
Write 7.3 3 1025 in standard notation.
The exponent is negative, so move the decimal
point 5 places to the left and add four zeros as
placeholders.
Build A Bridge 4
Write 9 3 1026 in standard
notation.
0.00007.3
7.3 3 1025 5 0.000073
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Guided Practice
1 What is a power of 10?
2 What is scientific notation?
3 Explain how to change a number from standard notation to scientific notation.
4 Explain how to change a number from scientific notation to standard notation.
For Numbers 5–7, change the number from standard notation to scientific
notation.
5 0.049 6 1,250 7 0.00015
For Numbers 8–10, change the number from scientific notation to standard
notation.
8 3.6 3 105 9 7.04 3 1022 10 2 3 107
11 The distance around the Earth at the equator is about 24,900 miles. How is that
number written in scientific notation?
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Practice
1 Circle the numbers below that are correctly written in scientific notation.
56.1 3 1024
3.8 3 1016
1.925 3 128 9.07 3 105
1.4 3 2107
60.2 3 106
2.03 3 1010 8 3 1023
For Numbers 2–7, change the number from standard notation to scientific
notation.
2 164,000 5 0.00071 3 0.01891 6 2,540,000 4 30,000,000
7 0.0000000673
For Numbers 8–13, change the number from scientific notation to standard
notation.
8 4.33 3 105 AL8 © 2009 Buckle Down – Options Publishing. COPYING IS FORBIDDEN BY LAW.
11 6.6 3 1029 9 8 3 1026
12 5 3 1011 10 9.05 3 108
13 2.8077 3 10212
14 The blue whale, believed to be the largest animal ever to have lived, can weigh
up to 4 3 105 pounds. How is that number written in standard notation?
15 A nanosecond is 0.000000001 of a second. How is that number written in
scientific notation?
16 Marianna is a chemistry student at Jacksonville State University in Jacksonville,
Alabama. Under her microscope, she observes an organism that has a mass of
4.1 3 1025 grams. Express this number in standard notation.
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