1. Scientific Notation
THE LOGICAL APPROACH

2. Warm Up
Write each number in standard notation.
2.54 x 102
6.7 x 102
1.14 x 103
Write each number in scientific notation.
75,000,000
208
907,100

3. Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000

4. Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01
10-3 = 1/1000 = 0.001
10-4 = 1/10000 =

5. Scientific Notation
We use the idea of exponents to make it easier to work with large and small numbers.
10,000 = 1 X 104
250,000 = 2.5 X 105
Count places to the left until there is one number to the left of the decimal point.
230,000 = ?
35,000 = ?

6. Scientific Notation Continued
= 6 X 10-5
= 4.5 X 10-4
Count places to the right until there is one number to the left of the decimal point
0.003 = ?
= ?

7. Multiplying with Scientific Notation
Add the Exponents
102 X 103 = 105
100 X 1000 = 100,000

8. Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103)
230 X 3300
Multiply the Coefficients
2.3 X 3.3 = 7.59
Add the Exponents
102 X 103 = 105
7.59 X 105
759,000

9. Multiplying with Scientific Notation
(4.6 X 104) X (5.5 X 103) = ?
(3.1 X 103) X (4.2 X 105) = ?

10. Dividing with Scientific Notation
Subtract the Exponents
104/103 = 101
10000X 1000 = 10

11. Dividing with Scientific Notation
(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

12. Dividing with Scientific Notation
(4.6 X 104) / (5.5 X 103) = ?
(3.1 X 103) / (4.2 X 105) = ?