Scientific Notation

Pages 26-27 of notebook

Essential question: How do I write small and large numbers using scientific notation?

Objective: I can write numbers in scientific notation.

What is scientific Notation?

Scientific notation is a way of expressing really big numbers or really small numbers.

It is most often used in “scientific” calculations where the analysis must be very precise.

Why use scientific notation?

For very large and very small numbers, these numbers can be converted into scientific notation to express them in a more concise form.

Numbers expressed in scientific notation can be used in a computation with far greater ease.

Scientific notation consists of two parts:

A number between these two numbers:

greater than or equal to 1

and less than 10

A power of 10

N x 10x

Powers of 10 page 28

102= 10 x 10 = 100

103

= 10 x 10 x 10 = 1,000

105 = 10 x 10 x 10 x 10

= 100,000

101= 10 = 10

104

= 10 x 10 x 10 x 10= 10,000

x 10

Powers of 10 page 28

100= 10 = 1

10-1= 10 x 1/100 = 1/10

10-2= 10 x 1/1000 = 1/100

104= 10 x 1/10000 = 1/1,000

109

= 1,000,000,000How many zeros follow the 1?

x 1/10

How many zeros in front of the 1?10-9

Powers of 10

Show thepowers of 10 video clip here...

To change standard form to scientific notation…

Place the decimal point so that there is one non-zero digit to the left of the decimal point.

Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10.

Continued… If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

Changing standard form to scientific notation.

Scientific NotationScientific notation has the form:

c x 10n

Between 1 and 10

Integer

Is it scientific notation? Yes or no?

52 x 109

3.56 x 105

3 x 105.6

0.7 x 106

No!

No! No!

Yes!

Scientific NotationThese numbers are written in scientific notation. What are they equal to?

7.2 x 105

= 7.2 x 100,000= 72 .0 0 0 0

= 720,000

.

Scientific NotationThese numbers are written in scientific notation. What are they equal to?

8.3506 x 107

= 8.3506 x 10,000,000= 8 3 5 0

60 0 0

= 83,506,000

..

Example 1

Given: 289,800,000 Use: 2.898 (moved 8 places) Answer: 2.898 x 108

Example 2

Given: 0.000567 Use: 5.67 (moved 4 places) Answer: 5.67 x 10-4

Changing scientific notation to standard form.

To change scientific notation to standard form…

Simply move the decimal point to the right for positive exponent 10.

Move the decimal point to the left for negative exponent 10.

(Use zeros to fill in places.)

Example 3

Given: 5.093 x 106

Answer: 5,093,000 (moved 6 places to the right)

Example 4

Given: 1.976 x 10-4

Answer: 0.0001976 (moved 4 places to the left)

PracticeWhat is the value of each scientific notation expression?

1. 2.83 x 10

2. 7 x 10

3. 5.11 x 10

4. 9.2057 x 10

= 283,000

= 7,000,000

= 51,100

= 92,057,000,000

5

6

4

10

Put a comma

after

every 3

numbers

(from the

right)

Review

1. 3.587 x 102. 567 x 1,0003. 76.12 x 1,0004. 0.903 x 100,0005. 0.0045 x 10,000

= 35.87= 567,000= 76,120= 90,300= 45

Work BackwardsWrite the number in scientific notation:

1. 907,000

2. 80,000,000

3. 3,876,100

4. 5917

36,700,000.7 spaces

= 3.67. 7x 10

= 9.07 x 10

= 8 x 10

= 3.8761 x 10

= 5.917 x 10

5

7

6

3

Try these on your whiteboards.