5.4 Scientific Notation

• Goals:

1.) To write numbers in scientific notation

2.) To multiply and divide scientific notation

Scientific Notationa shortcut for very large/small numbers

• The distance from earth to the north star is 10,000,000,000,000,000,000 meters.

• Fewer errors if we write as 1.0 x 1019 ?

Given a # in Standard Notation write it in Scientific Notation

1. Move decimal until the # is 1 ≤X <10

2. Then mult. that # by 10 to a power

3. The power will be the # of times you moved the decimal (if u moved to the rt it’s a neg. exp. If u moved to the lft it is a positive exp.)

Scientific NotationWrite an equivalent expression

using scientific notation:

3,200 3.2 103

Must be at least 1.0 and no more than 9.9999…

Scientific NotationWrite an equivalent expression

using scientific notation:

0.0307 3.07 10-2

Must be at least 1.0 and no more than 9.9999…

Change from scientific notation to standard form:

move the decimal the same amt of times as the exp. (if the exp + move to the right and if the exp is –

move to the left)

1.25 x 103

1250

Change from scientific notation to standard form:

7.0 x 105

700,000

Change from scientific notation to standard form:

4.8 x 10-3

0.0048

Change from scientific notation to standard form:

1.8 x 10-4

0.00018

Multiply Using Properties

(3.0 x 105)(4.1 x 10-

3)12.3 x 102

1.23 x 103

Divide Using Properties.Show your answer in scientific notation

6

7

100.5

105.2

6

7

10

10

0.5

5.2

0.5 x 10-

13

5.0 x 10-

14

Divide Using Properties.Show your answer in scientific notation

2

5

101.2

102.4

2.0 x 103

Divide Using Properties.Show your answer in scientific notation

2

5

100.9

107.2

0.3 x 107

3.0 x 106

Homework

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