1.1. Which is greater 5Which is greater 533 or 3 or 344? ?

2.2. 3.54 x 1000 =3.54 x 1000 =

1.1. Which is greater 5Which is greater 533 or 3 or 344? ?

2.2. 3.54 x 1000 =3.54 x 1000 =

53 = 125

34 = 81

3,540

4.84.8

Scientific Notation

Scientific Notation

Writing NumbersWriting NumbersScientific notation is used to write

very large and very small numbers. Today we will focus on only the larger numbers – using positive exponents.

The distance to the sun is 150,000,000 km

or 1.5x108 km.

Writing in Scientific NotationWriting in Scientific Notation

10ma1 10a

In scientific notation, a number is written using “POWERS OF 10’s”

Let’s investigate using these powers to understand the pattern.

1

10 10 101

100

1000

10,000

100,000 10x10x10x10x10 105

Look for patterns and complete the chart.

1 1 100

10 10 101

100 10 x 10 102

1000 10 x 10 x10 103

10,000 10x10x10x10 104

100,000 10x10x10x10x10 105

What seems to be the relationship between the exponent and the number written in factored form?

1 1 100

10 10 101

100 10 x 10 102

1000 10 x 10 x10 103

10,000 10x10x10x10 104

100,000 10x10x10x10x10 105

What seems to be the relationship between the exponent and the number written in decimal form?

Scientific Notation VideoScientific Notation Video

Exponents and Scientific NotationExponents and Scientific Notation

A number in scientific notation has two parts:

A number greater than or equal to 1, but less than 10 multiplied by a

power of ten

Moving PlacesMoving Places 4x103 = 4x10x10x10 = 4x1000 = 4000

Notice: the exponent on the 10 is 3 and the decimal after the 4 moved to the right 3 spaces.

2.3x105 = 230,000 moving the decimal right 5 spaces.

2.3x105 is scientific notation and 230,000 is decimal notation (or standard form).

EXAMPLE 1 Writing Numbers in Scientific Notation

Stars

There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation.

SOLUTION

Standard form300,000,000,000

Scientific notation3 1011

Exponent is 11.

ANSWER

The number in scientific notation is 3 x 1011.

Move decimal point 11 places to the left.

Try theseTry these

Write each in scientific notation

1) 320,000,000

2) 45,900

3) 20,000,000,000

4) 38 million

38,000,000

5) 9.22 million

9,220,000

Try theseTry these

Write each in scientific notation

1) 320,000,000

2) 45,900

3) 20,000,000,000

4) 38 million

38,000,000

5) 9.22 million

9,220,000

1. 3.2 x 108

2. 4.59 x 104

3. 2 x 1010

4. 3.8 x 107

5. 9.22 x 106

Try theseTry these

Write each in standard form

1) 8.9 x 105

2) 5 x 104

3) 8.345 x 108

4) 2.9 x 101

5) 5 x 100

Try theseTry these

Write each in standard form

1) 8.9 x 105

2) 5 x 104

3) 8.345 x 108

4) 2.9 x 101

5) 5 x 100

1. 890,000

2. 50,000

3. 834,500,000

4. 29

5. 5

Explain why these example are NOT in scientific notation. Be specific!

1) 38.6 x 105

2) 5.2 + 108

3) 10 x 1012

4) 0.4 x 106

Calculator notationCalculator notation

Some calculators show Some calculators show scientific notation the same scientific notation the same way we have written them way we have written them here. here.

Some use EE. They write Some use EE. They write 3.456 EE5 to mean 3.456 x103.456 EE5 to mean 3.456 x1055..

Some write the same thing with Some write the same thing with this in the screen 3.45605this in the screen 3.456050505..

HomeworkHomework

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