1. Scientific Notation

Every positive number X can be written as:

(1 < N < 10) x 10some positive or negative integer

Where N represents the numerals of X with the decimal point after the first nonzero digit.

2. Positive Exponents

101 = 10102 = 10X10= 100103 = 10X10X10 = 1000104 = 10X10X10X10 = 10,000

3. Negative Exponents

10-1 = 1/10 = 0.110-2 = 1/100 = 0.0110-3 = 1/1000 = 0.00110-4 = 1/10000 = 0.0001

4. 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 = ?

2.3 x 105

3.5 x 104

5. Scientific Notation Continued

0.00006 = 6 X 10-5

0.00045 = 4.5 X 10-4

Count places to the right until there is one number to the left of the decimal point

0.003 = ? 0.0000025 = ?

3 x 10-3

2.5 x 10-6

Multiplying with Scientific Notation

Add the Exponents

102 X 103 = 105

100 X 1000 = 100,000

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

Multiplying with Scientific Notation

(4.6 X 104) X (5.5 X 103) = ?

(3.1 X 103) X (4.2 X 105) = ?

Dividing with Scientific Notation

Subtract the Exponents

104/103 = 101

10000X 1000 = 10

Dividing with Scientific Notation

(3.3 X 104)/ (2.3 X 102)

33000 / 230 = 143.4783

Divide the Coefficients

3.3/ 2.3 = 1.434783

Subtract the Exponents

104 / 102 = 102

1.4347823 X 102

143.4783

Dividing with Scientific Notation

(4.6 X 104) / (5.5 X 103) = ?

(3.1 X 103) / (4.2 X 105) = ?