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```2-2 Powers of Ten and Scientific Notation
Warm Up
Problem of the Day
Lesson Presentation
Course 2
2-2 Powers of Ten and Scientific Notation
Warm Up
Find each value.
1. 92
81
2. 122
144
3. 152
225
4. 102
100
5. 103
1,000
6. 104
10,000
Course 2
2-2 Powers of Ten and Scientific Notation
Problem of the Day
Each day, Lowell runs one more lap than
he did the day before. After seven days
he has run 77 laps. How many laps did
he run on the first day?
8
Course 2
2-2 Powers of Ten and Scientific Notation
Learn to express large numbers in
scientific notation.
Course 2
of Ten and
Scientific
2-2 Powers
Insert Lesson
Title
Here Notation
Vocabulary
standard form
scientific notation
Course 2
2-2 Powers of Ten and Scientific Notation
The distance from Venus to the Sun is over
100,000,000 kilometers. You can write this
number as a power of ten by using a base of
ten and an exponent.
10 · 10 · 10 · 10 · 10 · 10 · 10 · 10 = 108
Power of ten
Course 2
2-2 Powers of Ten and Scientific Notation
The table shows several powers of ten.
Power of 10
Course 2
Meaning
Value
101
10
10
102
10 · 10
100
103
10 · 10 · 10
1,000
104
10 · 10 · 10 · 10
10,000
2-2 Powers of Ten and Scientific Notation
Additional Example 1: Multiplying by Powers of Ten
Multiply 14 · 103.
14 · 103 = 14 · (10 · 10 · 10)
= 14 · 1,000
= 14,000
Course 2
Use 10 as a factor
3 times.
Multiply.
Powers Lesson
of Ten and
Scientific
2-2 Insert
Title
Here Notation
Try This: Example 1
Multiply 12 · 102.
12 · 102 = 12 · (10 · 10)
= 12 · 100
= 1,200
Course 2
Use 10 as a factor
2 times.
Multiply.
2-2 Powers of Ten and Scientific Notation
You can also find the product of a number
and a power of ten simply by moving the
decimal point of the number. For powers of
ten with positive exponents, move the
decimal point to the right.
Course 2
2-2 Powers of Ten and Scientific Notation
Additional Example 2: Multiplying by Powers of Ten
Mentally
Find each product.
A. 212 · 104
4 places
212 · 104 = 212.0000
= 2,120,000
B. 31.6 · 103
31.6 · 103 = 31.600
= 31,600
Course 2
Move the decimal point
4 places.
4 zeros.)
3 places
Move the decimal point
3 places.
2 zeros.)
Powers Lesson
of Ten and
Scientific
2-2 Insert
Title
Here Notation
Try This: Example 2
Find each product.
A. 22.5 · 102
2 places
22.5 · 102 = 22.50
= 2,250
B. 39.5 · 103
39.5 · 103 = 39.500
= 39,500
Course 2
Move the decimal point
2 places.
1 zero.)
3 places
Move the decimal point
3 places.
2 zeros.)
2-2 Powers of Ten and Scientific Notation
Numbers are usually written in standard form.
For example, 17,900,000 is in standard form.
Scientific notation is a kind of shorthand that
can be used to write large numbers. Numbers
expressed in scientific notation are written as the
product of two factors. In scientific notation,
17,900,000 is written as
A number greater
than or equal to 1 but
less than 10
Course 2
A power of 10
2-2 Powers of Ten and Scientific Notation
Writing Math
In scientific notation, it is customary to use
a multiplication cross () instead of a dot.
Course 2
2-2 Powers of Ten and Scientific Notation
Additional Example 3A: Writing Numbers in Scientific
Notation
Write the number in scientific notation.
A. 4,340,000
6 places
Move the decimal point to
4,340,000 = 4,340,000 get a number that is greater
than or equal to 1 and less
than 10.
The exponent is equal to
= 4.34  106
the number of places the
decimal point is moved.
Course 2
2-2 Powers of Ten and Scientific Notation
Additional Example 3B: Writing Numbers in Scientific
Notation
Write the number in scientific notation.
B. 327,000,000
8 places
Move the decimal point to
327,000,000 = 327,000,000 get a number that is greater
than or equal to 1 and less
than 10.
= 3.27 
Course 2
108
The exponent is equal to
the number of places the
decimal point is moved.
Powers Lesson
of Ten and
Scientific
2-2 Insert
Title
Here Notation
Try This: Example 3A
Write the number in scientific notation.
A. 8,421,000
8,421,000 = 8,421,000
= 8.421  106
Course 2
6 places
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
The exponent is equal to
the number of places the
decimal point is moved.
Powers Lesson
of Ten and
Scientific
2-2 Insert
Title
Here Notation
Try This: Example 3B
Write the number in scientific notation.
5 places
B. 327,000
327,000 = 327,000
= 3.27 
Course 2
105
Move the decimal point to
get a number that is greater
than or equal to 1 and less
than 10.
The exponent is equal to
the number of places the
decimal point is moved.
2-2 Powers of Ten and Scientific Notation
Additional Example 4: Writing Numbers in Standard
Form
The population of China in the year 2000 was
estimated to be about 1.262  109. Write this
number in standard form.
Since the
9
1.262  10 = 1.262000000
exponent is 9,
move the decimal
point 9 places to
the right.
= 1,262,000,000
The population of China was about 1,262,000,000
people.
Course 2
Powers Lesson
of Ten and
Scientific
2-2 Insert
Title
Here Notation
Try This: Example 4
The distance from the Earth to the Sun is
calculated to be 1.5  108 kilometers. Write
this distance in standard form.
1.5  108 = 1.50000000
Since the exponent is
8, move the decimal
point 8 places to the
right.
= 150,000,000
The distance from the Earth to the Sun is about
150,000,000 kilometers.
Course 2
of Ten and
Scientific
2-2 Powers
Insert Lesson
Title
Here Notation
Lesson Quiz: Part 1
Multiply.
1. 25  102
2,500
2. 18  104
180,000
Find each product.
3. 110  102
11,000
4. 3.742  103 3,742
Course 2
of Ten and
Scientific
2-2 Powers
Insert Lesson
Title
Here Notation
Lesson Quiz: Part 2
Write each number in scientific notation..
5. 7,400,000 7.4  106
6. 45,000
4.5 104
7. Earth is about 9.292  107 miles from the Sun.
Write this number in standard form.
92,920,000
Course 2
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