# 2-2 Powers of Ten and Scientific Notation

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```					 2-2 Powers of Ten and Scientific Notation

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 Lesson Title Here Notation
Insert of Ten and Scientific

Vocabulary
Standard Form: a way to write numbers by using digits.
Example: three hundred sixty five in
standard notation is 365.
Scientific Notation: a method of writing very large or
very small numbers by using powers of 10.

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       Meaning         Value

101              10            10

102            10 · 10        100

103         10 · 10 · 10      1,000

104       10 · 10 · 10 · 10   10,000

Course 2
2-2 Powers of Ten and Scientific Notation

Example 1: Multiplying by Powers of Ten

Multiply 14 · 103.

14 · 103 = 14 · (10 · 10 · 10)   Use 10 as a factor
3 times.
= 14 · 1,000             Multiply.
= 14,000

Course 2
2-2 Insert Lesson Title Here Notation
Powers of Ten and Scientific

Try This: Example 1

Multiply 12 · 102.

12 · 102 = 12 · (10 · 10)   Use 10 as a factor
2 times.
= 12 · 100          Multiply.
= 1,200

Course 2
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

Example 2: Multiplying by Powers of Ten Mentally

Find each product.
A. 212 · 104                  4 places

212 · 104 = 212.0000      Move the decimal point
4 places.
= 2,120,000    (You will need to add
4 zeros.)
B. 31.6 · 103
3 places
31.6 · 103 = 31.600        Move the decimal point
3 places.
= 31,600        (You will need to add
2 zeros.)
Course 2
2-2 Insert Lesson Title Here Notation
Powers of Ten and Scientific

Try This: Example 2

Find each product.
A. 22.5 · 102              2 places

22.5 · 102 = 22.50      Move the decimal point
2 places.
= 2,250      (You will need to add
1 zero.)
B. 39.5 · 103
3 places
39.5 · 103 = 39.500     Move the decimal point
3 places.
= 39,500     (You will need to add
2 zeros.)
Course 2
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                        A power of 10
than or equal to 1 but
less than 10
Course 2
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

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

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.

The exponent is equal to
= 3.27    108   the number of places the
decimal point is moved.

Course 2
2-2 Insert Lesson Title Here Notation
Powers of Ten and Scientific

Try This: Example 3A
Write the number in scientific notation.
A. 8,421,000            6 places

Move the decimal point to
8,421,000 = 8,421,000     get a number that is greater
than or equal to 1 and less
than 10.
The exponent is equal to
= 8.421  106
the number of places the
decimal point is moved.

Course 2
2-2 Insert Lesson Title Here Notation
Powers of Ten and Scientific

Try This: Example 3B
Write the number in scientific notation.

B. 327,000              5 places

Move the decimal point to
327,000 = 327,000        get a number that is greater
than or equal to 1 and less
than 10.

The exponent is equal to
= 3.27    105    the number of places the
decimal point is moved.

Course 2
2-2 Powers of Ten and Scientific Notation

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
1.262  109 = 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
2-2 Insert Lesson Title Here Notation
Powers of Ten and Scientific

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
2-2 Powers Lesson Title Here Notation
Insert of Ten and Scientific

Assignment:
pg. 66 14-39
Left Column Only

Course 2

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