Ch 8: ExponentsE) Scientific Notation

Objective:

To simplify expressions involving scientific notation.

Key concepts:

1. Write expressions in Standard Form

2. Write expressions in Scientific Notation

3. Multiply scientific notation expressions

4. Divide scientific notation expressions

Scientific Notationused to write very large or very small numbers expressed in the form:

Definitions

Standard FormAn expression written without exponents

€

a ×10b

a number between 1.0 and 9.9

an integer

Example 1

Example 2

12 jumps to the right3,780,000,000,000 =

€

3.78 ×1012

7 jumps to the left0.00000064 =

€

6.4 ×10−7

RulesFrom Standard Form to Scientific Notation

1) Determine where the decimal should be placed 2) Count how many places from the “new” decimal point to the “old” decimal pointTo the RIGHT = (+) positive exponent

To the LEFT = (−) negative exponent

11 jumps to the right

4 jumps left

7 jumps to the right

Classwork

46,000,000

620,000,000,000

0.000538

0.000004

=

€

4.6 ×107

=

€

6.2 ×1011

=

€

5.38 ×10−4

6 jumps left=

€

4 ×10−6

1)

2)

3)

4)

Example 1

Example 2

RulesFrom Scientific Notation to Standard Form

1) Move the current decimal point the number of places based on the exponent as follows:(+) positive exponent = to the RIGHT

(−) negative exponent = to the LEFT

08.43000000

€

3.6 ×105

€

8.43 ×10−7

3.60000 360,000

0.000000843

=

=

5)

6)

7)

8)

€

2.64 ×109

€

3.41×10−6

€

4 ×108

€

7 ×10−6

2.640000000 2,640,000,000

3.41000000 0.00000341

400000000 400,000,000

7000000 0.000007

Classwork

=

=

=

=

RulesMultiplying Scientific Notation expressions

1) Multiply the numbers that have no exponents.

2) Add the exponents to calculate the new exponent for 10.

3) Verify that the result is in scientific notation

€

a ×10b

a number between 1.0 and 9.9

an integer

€

(2.1×108 )(1.5 ×106 )

€

2.1×108 ×1.5 ×106

(2.1)(1.5)

€

×

€

(108 )(106 )

€

3.15 ×1014

Example 1

€

19.142 ×1015

1 jump right

€

(5.63×107)(3.4 ×108)

(5.63)(3.4)

€

×

€

(107 )(108 )

€

1.9142 ×1016

+1

Example 2

Not in Scientific Notation

3.15

€

× 108+6

19.142

€

× 107+8

smaller bigger

Classwork9)

€

(8 ×1014 )(1.2 ×1011 )

€

9.6 ×1025

10)

€

(2.4 ×107)(4.9 ×109 )

€

11.76 ×1016

€

1.176 ×1017

1 jump right

+1

11)

€

(3.7 ×1010)(6.5 ×108 )

€

24.05 ×1018

€

2.405 ×1019

1 jump right

+1

12)

€

(9.7 ×10−6 )(8.6 ×10−5)

€

83.42 ×10−11

1 jump right

+1

€

8.342 ×10−10

smaller bigger

smaller bigger

smaller bigger

RulesDividing Scientific Notation expressions

1) Divide the numbers that have no exponents.

2) Subtract the exponents to calculate the new exponent for 10.

3) Verify that the result is in scientific notation

€

a ×10b

a number between 1.0 and 9.9

an integer

Example 1 Example 2

€

9.1×1012

3.5 ×107

€

9.13.5

×1012

107

=

€

2.6 ×1012− 7

=

€

2.6 ×105

€

5.074 ×1023

5.9 ×1011

€

5.0745.9

×1023

1011

=

€

0.86 ×1023−11

=

€

0.86 ×1012

1 jump left

−1

=

€

8.6 ×1011

smallerbigger

13)

€

(8.88 ×1019)(3.7 ×105)

14)

€

5.589 ×1024

8.1×1012

€

2.4 ×1014

€

0.69 ×1012

€

6.9 ×1011

1 jump left

−1

=

€

8.883.7

×1019− 5

€

5.5898.1

×1024 −12

Classwork

=

=

smallerbigger