1. SCIENTIFIC NOTATION Lesson 8-2 Review
A QUICK WAY TO WRITE
REALLY, REALLY BIG OR
REALLY, REALLY SMALL NUMBERS.

2. We can write multiples of 10’s using exponents
10000 = 10 x 10 x 10 x 10 = 104
= 10 x 10 x 10 = 103
= 10 x 10 = 102
= 101
1 = 100
Do you see a pattern?

3. Sooooo negative exponents come from multiplying tenths
= 10-1
= = 10-2
= = 10-3
= = 10-4

4. 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?

5. A number written in Scientific Notation
has three parts…
A number greater than one but less than ten
A power of ten
A multiplication sign

6. 1. Move the decimal to the right of the first non-zero number.
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.

7. Soooo
137,000,000 can be rewritten as
1.37 X 108

8. Using scientific notation, rewrite the following numbers.
Now You Try
Using scientific notation, rewrite the following numbers.
347,000.
902,000,000.
61,400.

9. Using scientific notation, rewrite the following numbers.
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

10. Convert these to standard notaion:
1.23 X X 106

11. Convert these to standard notaion:
1.23 X , X 106 6,806,000

12. 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

13. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers.

14. Using Scientific Notation, rewrite the following numbers.
Your Turn
Using Scientific Notation,
rewrite the following numbers.
8.82 X 10-4
5.9 X 10-7
4 X 10-5

15. .000007 The nucleus of a human cell is about
7 X 10-6 meters in diameter. What is the length in standard notation?

16. Proper Scientific Notation Which way did the decimal move?
You can think of this as going the opposite direction
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 =

17. 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 =
X =

18. You Try
55.6 x 10 4
.067 x 10 12
x 10 -8
23.1 x 10 -4
102 x 10 5
-2.3 x 10 3

19. Multiplication with Scientific Notation Lesson 8-3 Review

20. 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 Add the exponents
Answer: 6 x 102

21. Example Given: 2 (4 X 106) Multiply decimals: 2 X 4 = 8
Add Exponents: 100 x 106=100+6=106
Answer: X 106

22. Example
Given: 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: X 1014
Now, Rewrite in Scientific Notation if needed.
Final Answer:
1.36 X 1015

23. Given: (2 X 10-2) • (6 X 10-5) Your Turn 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

24. Assignment
 p. 402  7-25, 28-29, SImSo 49
Block 2: also p

25. Dividing Numbers in Scientific Notation
Lesson 8-5 continued

26. Dividing Numbers in Scientific Notation
Divide the decimal numbers.
Then subtract the exponents

27. Example 1
Given: 8 • 10-7
2 • 10-2
Divide decimals: 8÷2 = 4
Subtract exponents: (-7)-(-2)= -5
Final Answer: 4 •10-5

28. Example 2 Given: 1.6 X 103 8 X 104 Divide decimals: 1.6 ÷ 8= 0.2
Subtract exponents: =-1
Preliminary Answer: X 10-1
Now, Rewrite in Scientific Notation if needed.
Final Answer:
2.0 X 10-2

29. Your Turn
Given: 3.4 X 102
2 X 10-5
Divide decimals: ÷ 2= 1.7
Subtract exponents: 2- (-5) =7
Answer: X 107

30. Assignment
Block 1:  p
Both Blocks: p , SimSo 50