1. Scientific Notation

2. Scientific Notation 과학적 기수법
A short-hand way of writing
large numbers without
writing all of the zeros.

3. The Distance From the Sun to the Earth in miles
93,000,000

4. Step 1 93,000,000 = 9.3000000 Move decimal left
Leave only one number in front of decimal (one number to the left of the decimal).
93,000,000 =

5. Step 2
Write number without zeros
93,000,000 = 9.3

6. Step 3 7 93,000,000 = 9.3 x 10 Count how many places you moved decimal
Make that your power of ten
93,000,000 = 9.3 x 10 7

7. The power of ten is 7 because the decimal moved 7 places. 7
93,000,000 = 9.3 x 10 7

8. 93,000,000 --- Standard Form (Decimal form)
9.3 x Scientific Notation

9. Scientific notation Decimal notation Scientific notation 127
(정수)
Decimal notation
Scientific notation
127
1.27 x 102
0.0907
9.07 x 10 – 2
5.06 x 10 – 4
2.3 x 1012

10. Place Value Decimal System1 2 3 . 4 5 6 7
Millions
Hundred Thousands
Ten Thousands
Thousands
Hundreds
Tens
Ones
Tenths
Hundredths
Thousandths
Ten thousandths
Hundred Thousandths
Millionths
Ten Millionths
106
105
104
103
102
101
100
10-1
10-2
10-3
10-4
10-5
10-6
10-7 20
0.4
0.05
0.006
0.0007 `

11. When using Scientific Notation, there are two kinds of exponents: positive and negative
Positive Exponent:
2.35 x 108
Negative Exponent:
3.97 x 10-7

12. When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:
With a positive exponent, move the decimal to the right:
4.08 x 103 = 4 0 8
Don’t forget to fill in your zeroes!

13. When changing scientific notation to standard notation, the exponent tells you if you should move the decimal:
With a negative exponent, move the decimal to the left:
4.08 x 10-3 =
Don’t forget to fill in your zeroes!

14. An easy way to remember this is:
If an exponent is positive, the number gets larger, so move the decimal to the right.
If an exponent is negative, the number gets smaller, so move the decimal to the left.

15. The exponent also tells how many spaces to move the decimal:
In this problem, the exponent is +3, so the decimal moves 3 spaces to the right.

16. The exponent also tells how many spaces to move the decimal:
In this problem, the exponent is -3, so the decimal moves 3 spaces to the left.

17. When changing from Standard Notation to Scientific Notation:
1) First, move the decimal after the first whole number:
2) Second, add your multiplication sign and your base (10).
x 10
3) Count how many spaces the decimal moved and this is the exponent.
x 10 3 3 2 1

18. When changing from Standard Notation to Scientific Notation:
4) See if the original number is greater than or less than one.
If the number is greater than one, the exponent will be positive.
= x 105
If the number is less than one, the exponent will be negative.
= 6.72 x 10-8

19. Page 82 Try changing these numbers to proper Scientific Notation:
430
3,400,000
11.2 x 104
0.01 x 10-2
4.3 x 102
3.4 x 106
4.5 x 10-6
1.12 x 105
1 x 10-4

20. Rewrite these in decimal form Page 82

21. Multiplying with Scientific Notation
(5. X 102)(3.3 X 103)
Multiply the Coefficients
5 X 3.3 = 16.5
Add the Exponents
102 X 103 = 105
16.5 X 105
BUT 16.5 is not greater than or equal to 1 and less than 10.
so we must move the decimal place, 1.65 X 106

22. Practice Page 83 #1,2 Multiplying with Scientific Notation
(2.2 X 10-2) X (3 X 105) =
(-3.2 X 105) X (2.1 X 102) =
6.6x103
-6.72x107

23. Dividing with Scientific Notation
(3.3 X 104)/ (6.6 X 102)
3.3/ 6.6 = 0.5
Subtract the Exponents
104 / 102 = 102
0.5 X 102
BUT 0.5 is not greater than or equal to 1 and less than 10.
5 X 101
(3.3 X 104)/ (2.3 X 102)
33000 / 230 =
Divide the Coefficients
3.3/ 2.3 =
Subtract the Exponents
104 / 102 = 102
X 102

24. Dividing with Scientific Notation
(2.1 X 104) / (8.4 X 103) =
(3.1 X 103) / (6.2 X 105) =
2.5 x 100
5 x 10-3

25. Scientific Notation page 84 Addition/Subtraction

26. Homework
page 83 # 3-6 page 84 all