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SCIENTIFIC NOTATION
Lesson 8-2 Review
A QUICK WAY TO WRITE
REALLY, REALLY
BIG
OR
REALLY, REALLY SMALL
NUMBERS.
We can write multiples of 10’s
using exponents
10000 = 10 x 10 x 10 x 10 = 104
1000 = 10 x 10 x 10 = 103
100 = 10 x 10 = 102
10 = 101
0
1 = 10
Do you see a pattern?
Sooooo
negative exponents come from multiplying tenths
1
100
1
1000
1
10000
= 10-1
=
1
10
1
2
10
=
1
3
10
= 10-3
=
1
4
10
= 10-2
=
-4
10
Rules for Scientific Notation
To be in proper scientific notation
the number must be written with
* a number between 1 and 10
* and multiplied by a power of ten
23 X 105 is not in proper scientific
notation. Why?
A number written in Scientific Notation
has three parts…
A number
greater
than one
but less
than ten
2.110
A multiplication
sign
3
A power of
ten
To write a number in scientific notation:
1. Move the decimal to the right of the
first non-zero number.
2. Count how many places the decimal
had to be moved.
3. If the decimal had to be moved to the right,
the exponent is negative.
4. If the decimal had to be moved to the left,
the exponent is positive.
Soooo
137,000,000 can be rewritten
as
1.37 X
8
10
Now You Try
Using scientific notation,
rewrite the following numbers.
347,000.
902,000,000.
61,400.
Now You Try
Using scientific notation,
rewrite the following numbers.
347,000.
3.47 X 105
902,000,000.
9.02 X 108
61,400.
6.14 X 104
Convert these to standard
notaion:
1.23 X 105
6.806 X
6
10
Convert these to standard
notaion:
1.23 X 105
123,000
6
6.806 X 10
6,806,000
In the United States, 15,000,000
households use private wells for their
water supply. Write this number in
scientific notation.
1.5 X 107
Your Turn
Using Scientific Notation,
rewrite the following numbers.
0.000882
0.00000059
0.00004
Your Turn
Using Scientific Notation,
rewrite the following numbers.
0.000882
8.82 X 10-4
0.00000059
5.9 X 10-7
0.00004
4 X 10-5
The nucleus of a human cell is about
7 X 10-6 meters in diameter. What is
the length in standard notation?
.000007
Proper Scientific Notation
Which way did the decimal move?
If you move the decimal to the left: The exponent goes UP
88.2 X 103 =
8.82 X 10 ?
8.82 X 10 4
If you move the decimal to the right: The exponent goes DOWN
0.45 X 103 =
4.5 X 10 ?
4.5 X 10 2
154.7 X 10
-6
=
Proper Scientific Notation
Negative exponents follow the same rules
You can think of this as
going the opposite
direction
If you move the decimal to the left: The exponent goes UP
If you move the decimal to the right: The exponent goes DOWN
154.7 X 10
-6
0.048 X 10
=
-3
=
You Try
1.
55.6 x 10 4
2.
.067 x 10 12
3.
- 415.1 x 10 -8
4.
23.1 x 10 -4
5.
102 x 10 5
6.
-2.3 x 10 3
Multiplication with Scientific
Notation
Lesson 8-3 Review
Multiplication with Scientific Notation
• Multiply the decimal numbers together.
• Add the exponents to get the power of 10.
Sample Problem: Multiply (3 x 10-3) (2 x 105)
Solution: Multiply 3 x 2.
Add the exponents -3 + 5
Answer: 6 x 102
Example
• Given:
2 (4 X 106)
• Multiply decimals: 2 X 4 = 8
• Add Exponents: 100 x 106=100+6=106
• Answer: 8 X 106
Example
• Given:
•
•
•
•
•
3.4 X 105 • 4.0 X 109
Multiply decimals: 3.4 X 4.0 = 13.6
Add Exponents: 105 x 109=105+9=1014
Preliminary Answer: 13.6 X 1014
Now, Rewrite in Scientific Notation if needed.
Final Answer:
1.36 X 1015
Your Turn
• Given:
(2 X 10-2) • (6 X 10-5)
• Multiply Decimals: 2 X 6 = 12
• Add Exponents: 10-2 x 10-5=10-2+(-5)=10-7
• Answer: 12 X 10-7
• Rewrite in Scientific Notation
• Final Answer: 1.2 X 10-6
Assignment
p. 402 7-25, 28-29, SImSo 49
Block 2: also p. 407 22-27
Dividing Numbers in Scientific
Notation
Lesson 8-5 continued
Dividing Numbers in Scientific
Notation
• Divide the decimal numbers.
• Then subtract the exponents
Example 1
• Given: 8 • 10-7
2 • 10-2
• Divide decimals: 8÷2 = 4
• Subtract exponents: (-7)-(-2)= -5
•
Final Answer:
4 •10-5
Example 2
• Given: 1.6 X 103
8 X 104
• Divide decimals: 1.6 ÷ 8= 0.2
• Subtract exponents: 3 - 4 =-1
• Preliminary Answer: 0.2 X 10-1
• Now, Rewrite in Scientific Notation if needed.
• Final Answer:
2.0 X 10-2
Your Turn
• Given: 3.4 X 102
2 X 10-5
• Divide decimals: 3.4 ÷ 2= 1.7
• Subtract exponents: 2- (-5) =7
•
Answer: 2.81 X 107
Assignment
• Block 1: p. 407 22-27
• Both Blocks: p. 420 13-20, SimSo 50