Scientific Scientific NotationNotation

Algebra SeminarAlgebra Seminar

ObjectivesObjectives

►Write numbers in standard and Write numbers in standard and scientific notation.scientific notation.

►Perform calculations with numbers in Perform calculations with numbers in scientific notation.scientific notation.

What is Scientific Notation?What is Scientific Notation?

►A number expressed in the form:A number expressed in the form:

where where na 10× 101 <≤a

Example:

Neptune is 2,800,000,000 miles from the sun.

91082 ×.

How do you write a number in How do you write a number in scientific notation?scientific notation?

Ex: Ex: 3,000,000,000,0003,000,000,000,000

Where is the decimal point?

.

You move the decimal point to the left until the number in front of it is between 1 and 9.3,000,000,000,000

121003 ×= ...

How do you write a number in How do you write a number in scientific notation?scientific notation?

Ex: 0.000063Ex: 0.000063

You move the decimal point to the right until the number to the left of it is between 1 and 9.

0.000063

51036 −×= .

Notice that the exponent is negative!

Write in Scientific NotationWrite in Scientific Notation

234,000,000234,000,000

1. 1. 23.4 x 107

2. 2. 2.34 x 108

3. 3. 234 x 106

4. 4. 2.34 x 10-8

How to change numbers in How to change numbers in scientific notation to standard scientific notation to standard

notation.notation.►First, decide which way you are going First, decide which way you are going

to be moving your decimal point.to be moving your decimal point.

Negative Exponent – move to the left

Positive Exponent – move to the rightMove the decimal point the number of

the exponent.

Ex: 6.35 x 104 =

1.82 x 10-5 =

63,500

0.0000182

Write in standard notationWrite in standard notation

►9.608 x 109.608 x 1099

►3.5 x 103.5 x 10-4-4

►8.3 x 108.3 x 10-2-2

►5.07 x 105.07 x 1066

9,608,000,000

0.00035

0.083

5,070,000

Operations with scientific Operations with scientific notation.notation.

Adding:Adding: • You just add the first numbers

(4 x 104) + (9 x 104) = (4 + 9) x 104

= 13 x 104

Subtracting:Subtracting:• You just subtract the first numbers

(8 x 104) - (2 x 104) = (8 - 2) x 104

= 6 x 104

Operations with scientific Operations with scientific notation.notation.

Multiplying:Multiplying:• Multiply the first numbers and then the

second numbers.(7 x 102)(4 x 105) = (7 4)(102 105)

= 28 x 107

• Write 28 in scientific notation.

(2.8 x 101) x 107

• Simplify.

2.8 x 108

Operations with scientific Operations with scientific notation.notation.

Dividing:Dividing:• Divide the first numbers and then the

second numbers.

( )

3

858

5

8

5

1024

102410

10

2

48

102

1048

×=

×=⎟⎟⎠

⎞⎜⎜⎝

⎛×⎟⎠⎞

⎜⎝⎛=

×

× −−−−

−

−

−

.

...

Simplify the exponents.