1. Scientific Notation

2. Why and What?
Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction.
The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient.

3. Why and What? 6.023 x1023 What About 1 Mole:
602,300,000,000,000,000,000,000 OR
6.023 x1023

4. Why and What?
5.67 x 105
exponent
base
     coefficient
OR: 567,000

5. Basics COEFFICIENT must be greater or equal to one and less than 10.
BASE – always 10
EXPONENT – number of zeros before or after decimal in coefficient

6. Basics
100= 1
101= 10
102= 100
103= 1000
104= 10,000
105= 100,000
106= 1,000,000
107= 10,000,000
10-0= 1
10-2= .01
10-3= .001
10-4= .0001
10-5=
10-6=
10-7=

7. Basics – Changing Form Look at EXPONENT
Positive Exponent, move decimal exponent number of places to right.
Negative Exponent, move decimal exponent number of places to left
2.00 x 102 = 200.
2.00 X 10-2 =

8. Basics – Changing Form Decimal to SN format:
If you move decimal to right, exponent is negative
If you move decimal to left, exponent is positive
200. = 2.00 x 102
= 2.00 X 10-2

9. Adding/Subtracting Convert SN numbers to have SAME Exponent value
Add/Subtract Coefficients
Exponent stays the same
Reform sum/difference into correct SN by moving decimal and changing exponent

10. Multiplication
Scientific notation provides a place to hold the zeroes that come after a whole number or before a fraction. The number 100,000,000 for example, takes up a lot of room and takes time to write out, while 108 is much more efficient.
                                                                                                      
Model: (2 x 102) x (6 x 103) = 12 x 105 = 1.2 x 106

11. Multiplication Multiply Coefficients ADD exponents
Reform into correct SN by moving decimal and changing exponent

12. Division
Section F: Division (a little harder - we basically solve the problem as we did above, using multiplication. But we need to "move" the bottom (denomenator) to the top of the fraction. We do this by writing the negative value of the exponent. Next divide the first part of each number. Finally, add the exponents).
(12 x 103) Model: = 2 x (103 x 10-2) = 2 x 101 = 20 (6 x 102)

13. Division
Divide coefficients
SUBTRACT exponents
Reform into SN

14. Converting to SN
1.  
50000
2.  
60,000,000
3.  
4.  
0.0004
5.  
461,000.00
6.  
7.  
8.  
9.  
51,200,000,000
10.  
11.  
210,000,000,000
12.  
13.  
14.  
4,900,000,000,000
15.  
16.  
17.  
18.  
6,340,000
19.  
20.  
21.  
36,300,000,000

15. Converting to Decimal 1. 7 x 107 2. 5 x 10-4 3. 8 x 10-5 4. 2 x 106 5.
1.  
7 x 107
2.  
5 x 10-4
3.  
8 x 10-5
4.  
2 x 106
5.  
9.77 x 104
6.  
2.1 x 10-12
7.  
8 x 108
8.  
2.03 x 10-9
9.  
4.3 x 10-7
10.  
8.13 x 109
11.  
2.6 x 10-6
12.  
8.4 x 1012

16. Adding & Subtracting 1. ( x 10-6) (1.3 x 10-8) 2.
1.  
( x 10-6) (1.3 x 10-8)
2.  
(9 x 104)  +  (3.5 x 105)
3.  
(9 x 10-7)  +  (8 x 10-7)
4.  
(8.5 x 106)(5 x 107)
5.  
(7 x 105)  -  (9.4 x 105)
6.  
(2.5 x 10-6)(6 x 10-6)(5 x 10-7)