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BELL WORK

• How many space do you move the decimal to make it whole number?

0.002

3 spaces

• How many spaces do you move the decimal to make it 4?

4000000

6 spaces

42510011 0010 1010 1101 0001 0100 1011

Section 8.4Scientific Notation

April 22, 2010

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What Will We Learn Today?

• How to represent and interpret numbers using scientific notation

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Take A Guess…

• Do you know this number, 300,000,000 m/sec.?

• It’s the speed of light!

• What is Avogadro’s number?• 602,200,000,000,000,000,000,000,000

- 23 zeros!!

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• Scientists have developed a shorter method to express very large numbers. This method is called scientific notation. Scientific Notation is based on powers of the base number 10.

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Scientific Notation

100 =

101 =

102 =

103 =

104 =

105 =

Do you see a pattern?

exponent 2, two zeros

exponent 0, no zeros exponent 1, one zero

exponent 3, three zeros

exponent 4, four zeros

exponent 5, five zeros

1

10010

1000

10000100000

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Back to Avogadro’s number

602200000000000000000000000

How many zeros?

How would you write it?

What about the 6022?

- becomes 6.022 x 1023

1023

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The number 123,000,000,000 in scientific notation is written as…

The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and less than 10.

The second number is called the base. It must always be 10 in scientific notation. The base number 10 is always written in exponent form.

x 1011

1.23

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How to write a number in scientific notation:

• Begin with 123,000,000,000

– Put the decimal after the first digit and drop the zeroes.

1.23000000000- Count and move decimal over to the left until last zero

1.23000000000- Since the decimal can be moved over 11 spots to the

left, the exponent is11

GOAL:

_________ x 10

coefficient

1.23___exponent

11

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With your partner try these…

1). 8000

8 x 103

2). 65000000000

6.5 x 1010

3) 14000000

14 x 107

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What is this number?

• Do you recognize this number,

0.000000000753 kg. ?

• It’s the mass of a dust particle!

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How to write a really small number in scientific notation

Begin with 0.00000225

- Put the decimal after the first number other than zero (boxed area becomes coefficient)

0.000002.25- Count how many spaces the decimal is moved to

the right (this become a negative number which is the exponent)

GOAL:

_________ x 10

coefficient

2.25___exponent

-6

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When to use a positive exponent

• POSITIVE EXPONENT

– For very BIG, LARGE, HUGE, numbers such as…

1). World population 5 x 109 or 5,000,000,000

2). Seconds in a year 3 x 107 or 30,000,000

3). Average hairs on head 2 x 106 or 2,000,000

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When to use a negative exponent

• NEGATIVE EXPONENT

- For very SMALL, TINY, MICROSCOPIC numbers 1). Time taken by light to travel one meter 3 × 10-9 (seconds)

or 0.000000003 seconds 2). The charge on an electron 1.6 × 10-19 C

or 0.00000000000000000016 Celsius

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With your partner try these…

1). 0.00000059

5.9 x 10-7

2). 0.507

5.07 x 10-1

3) 0.04

4 x 10-2

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Carousel

• Get with your group and work together to solve the questions at each station.

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Journal Time

• Write in your own words when you would use a positive exponent and when you would use a negative exponent

• Explain how using scientific notation might be useful for you in real life

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Homework

• In text: # 1- 21 odd, 34-52 even, 60-70 all

• All Due Tomorrow